| Sajha.com Archives | |
| Username | Post |
| Robert Frost | Posted
on 22-Jan-03 03:54 AM
Three blindfolded people, A, B, and C, each take one hat from a barrel containing three black and two white hats. A and B remove their blindfold and can then see the hats on the heads of the other two, but not the hat on their own head. A says, "I cannot tell what the color of my own hat is." Upon hearing this, B says: "I cannot tell the color of my hat either." Hearing these two statements, C, who is still blindfolded, says: "Now I know what color my hat is." How did he know, and what was the color of his hat?? Now I invite the logics of Sajha. Please provide reasons to support your answers. |
| PremPujari | Posted
on 22-Jan-03 04:12 AM
aaaaaaanch ROBERTjyu, maile ta try ni garina ni hehe..!! Gunajyu le bhanya jastai, Hisaab bhaneshi pisaaap aaune American jastai Logic bhaneshi allergic huune Nepali pariyo hehe!! malai ta aayena. Are you sure this is not racist puzzle? B and C must have same colored hat. when A looks at B -- no that doesn't make sense. what the.... ma sochna thaali ra!! oops. :) aayena |
| Poonte | Posted
on 22-Jan-03 05:03 AM
Jhandai malai PP le jityo bhanera saato-futlo udyo ni mero yaar...eheheh...ke ho, PP? Bihana 5 baje nai uthne jahile ni? Suryasta mai Hudson tira snaan garne ho ki ke ho? Robert jyu le ni kya jhella gardyo...hijo ko jaand ni utrya thiyena...ahile aba 3 ghanta drive garnu chha...ringaidiyo ni saberai! Tei pani puzzle bhanesi gas ko nozzle bata hutututu petrol aako jastai, mero "nozzle" bata hututututu soo soo faalesi, ani nuhayera puja-paath sidhesi yesso bichar gareko, hijo ko tyo golveda ko achar le ho ki ke ko, magaj ma fyatta aai halyo ni jawaf: IT'S BLACK! C is wearing a black hat!!! Why? 'Cause my mommy said so :P For either A or B to not know what the colors of their own respective hats are, only either of the two is possible: 1. the ones that they see are black and black, 2. the ones they see are black and white. (Because, had they seen white and white, and since there are only two whites, either of them would have known that the one on his/her own head is black.) Assume A sees black and black (on B and C) [condition 1 above]...now, B can only see one black and one white on either A or C [condition 2 above]...now, since A has already seen black on C, A can only be wearing white! Hence, C is wearing black! Assume B sees black and black (on A and C)...[use the same logic above]...C is still wearing black! Voila!!! Let me hit the road now...aekchhin ma feri rush hour ko tanta shuru hunchha natra... |
| PremPujari | Posted
on 22-Jan-03 06:11 AM
ke re?? POO DAI? Kasto ringaaako??? Come again!!! TIRIMIRIJHYAAI!!! |
| noname | Posted
on 22-Jan-03 06:43 AM
I knew…POONTE was after something. I had seen him going to SAJHACHAUR with 5 CAPS and 3 LINGAS. :) POOLICE KO BANDUK ra MERO COMPUTER KO TAL USTAI…THYAKKAI MAUKA MA FISSA…garidine. Simple Bhasama: Both B and C cannot have white caps (otherwise A could have figured it out that his was black). So either both B and C or one of them have Black cap. Had C been wearing white cap, B could have figured out that his is not white (remember both can not have white). B could not figure out his cap. C MUST HAVE BLACK CAP. |
| noname | Posted
on 22-Jan-03 06:48 AM
Here is one more (though simpler than earlier): The terrorists in rural side of Nepal are detaining you. There are only two doors in otherwise closed house. One of these, you know not which, leads to freedom and the other to execution. In front of each door there is a guard. All you know is that one of these guards always tells the truth and the other one always lies. Of course the guards know which door is which and which of them is a liar and which always tells the truth. You are permitted to ask one of the guards a simple yes/no question and then pass through the door of your choice. What question should you ask, that will guarantee that you can correctly choose the door to freedom? |
| DWI | Posted
on 22-Jan-03 02:54 PM
WOW, Puzzles. Anything involving logic. Good one Robert Frost, I know mr. Poonte would crack it. I like noname's puzzle, unfortunately I was able to crack it too. I think I had heard a similar one. Noname, Should I give away the answer? |
| Robert Frost | Posted
on 22-Jan-03 03:23 PM
Yes, Poonte da man. Though I like noname's logic but in order for C to know what hat he is wearing, the other two has to be wearing white hats. Since there are only two white hats. Noname, Goddam! hehe. Let me get back to you :) In the meantime, here is something for all, its called, THE OLDEST HAS RED HAIR The following coversation takes place between two friends A and B, who have not seen each other for a long time. A: I have three sons. B: How old are they? A: The product of their ages is 36. B: That is not enough information to answer my question. Can you give me another clue? A: Yes, their ages are integer numbers whose sum is the same as the number you see on the store across the street. B: Give me a few minutes to work it with pen and pencil. B: (a few minutes later) I have almost got the answer but I need another clue. A: O.K. The oldest has red hair. B: I have got it. What are the ages of the three sons?? LETS SOLVE IT ! |
| sagarmatha | Posted
on 22-Jan-03 03:51 PM
2,2,9 How did I know? I was present there at that time and the number in the store was 13. Could have been 1-6-6 too if the oldest one had a twin brother. |
| SITARA | Posted
on 22-Jan-03 03:52 PM
GRE Quizes!!!... Mad memories Frost ji! :( Loved your poems more! :) hehe! Actually watching everyone have a go at the puzzles! Thanks! A definite change from the usual threads. |
| noname | Posted
on 22-Jan-03 05:34 PM
RF.........same source? DWI..........some more puzzles...if not answers!! |
| Robert frost | Posted
on 22-Jan-03 08:33 PM
What hapenned to the logics of Sajha? :( Comon lets do it!!!! |
| PremPujari | Posted
on 22-Jan-03 09:06 PM
1*1*36>> sum is 38 1*2*18 >> sum is 21 1*3*12 >> sum is 16 1*4*9 >> sum is 14 1*6*6 >> sum is 13 2*2*9 >> sum is 13 2*3*6>> sum is 11 3*3*4>> sum is 10 that friggin' B looked at the number at the door across the street, and yet he couldn't figure out the number because two of the sum is same ie 13. so choices are, 1-6-6 and 2-2-9 both having sum 13. B was confused here, so he wanted further info. He was told the Oldest has a red hair, that means there is one OLDEST, unlike 1-6-6, which has oldest is the twins. So the choice is 2-2-9. old hair chai robert jyu is saying he has red hair. :D |
| Robert Frost | Posted
on 22-Jan-03 10:00 PM
PP bro and Sagarmatha, you guys hit the bull's eye. PP bro, I have a black hair and just for you, I happen to be the oldest son in the family. Time for another one?? Here you go!! Two trains 100 miles apart are on the same track heading towards each other at 50 miles per hour. At this moment a bee moving at 75 miles per hour flies from the front of one train to the front of another. After landing he immediately reverses course heading for the first train. He repeats this back and forth motion going a shorter and shorter distance with each trip from train to train until he is crushed in the collison of the two trains. How far did he fly? |
| Baba | Posted
on 22-Jan-03 10:07 PM
I have no clue but i go for 6,6,1 situation. Here is what I think, situation possible ages sum of ages 1 36,1,1 38 2 18, 2,1 21 3 9,4,1 14 4 9,2,2 13 5 6,6,1 13 6 6,3,2 11 7 4,3,3 10 situations 4 and 5 add up to 13 and therefore the clue about red hair is useful. otherwise it would not have been possible to answer with only one more clue. It shows that old one is only diffrentiated by hair color so they should be twins!! + i didnot use the number of the shop!!!! oops i don't know how it works but any way I already typed so i decided to post. |
| Baba | Posted
on 22-Jan-03 10:17 PM
Oops Again another! Let me sleep after this. since two trains meet at the mid way - 50 miles away after exactly one hour, the bee has exactly one hour to fly before he gets crushed. so he should travel 75 miles at that time. |
| arch119 | Posted
on 22-Jan-03 10:23 PM
Footnote - N.B (1) Implicit in my proof is the assumption that B made his statement after thoroughly listening to A. N.B (2) about PROOF by contradiction -if we suppose that a statement (called Proposition by logicians) can either be TRUE or False and nothing in between, then this method of proof is very effective . what we do is , suppose that the Statement we have to prove is False...and then by reasoning (what Holmes would say "art of deduction" and Hercule Poirot would say "using one's grey cells"), we get to a contradiction to an already KNOWN FACT.So our supposition of Falsity of the statement to be proved is inappropiate and hence our statement must be TRUE. |
| arch119 | Posted
on 22-Jan-03 10:23 PM
The color of C's hat is BLACK and this is why....... here is an attempt to prove this by contradiction (for those unfamiliar with this method of proof pls see the footnote), Lets suppose that the color of C's hat is WHITE, (1) As A said, "I cannot tell what the color of my own hat is.", the color of B's hat should have been BLACK ( reason :- had the color of B's hat been WHITE, A would have known that the color of his hat is 'BLACK' as there are only 2 WHITE hats and he is seeing both of them on B and C's heads). (2)Now, B listened to A's statement and B can see C's hat too (which is WHITE in color).So he knows that he has a BLACK hat (reason:- he knows that - had the color of his hat been WHITE , A wouldnt have told the statement he just said ,coz A would have known the color of his hat ,had he(B) himself and C both had WHITE hats!!!). (3) Now , we have a contradictoin....if C had a WHITE hat, B could (easily) have said that the color of his hat is BLACK but according to the puzzle presented by Robert Frost bro,B was himself not sure of the color of his hat after listening to A's statement. So , if we suppose that the puzzle is "valid", C couldnt have had "WHITE" hat,so by contradiction, C must have had a "BLACK" white. please see my next posting for footnote |
| nhuchche | Posted
on 22-Jan-03 10:24 PM
http://www.sukuti.com/archives/articles/2275.htm has the answer to the first question. |
| Baba | Posted
on 22-Jan-03 10:34 PM
I too have one. You can try New Year's Resolutions It's traditional on New Year's Eve to announce your New Year's resolutions, those things that you're going to do better or more of during the new year. The four couples who met at Mark's place for New Year's eve made no exception to this tradition. Each couple announced their resolutions for the New Year, vowing that this year, they would do them. To help them with this goal, each made their resolution a specific, achievable goal, rather than the ethereal "I'll do more" kind of resolution. Determine the full name of each couple and the New Year's resolution each couple announced. 1. Tom and his wife were determined to take their kids camping during the summer this year. 2. Mr. Club, who wasn't Greg, announced that they were planning to exercise at least twice a week. Martha wasn't married to Mark. 3. Sam didn't plan to buy a new home. Carol Diamond didn't plan to lose 30 pounds. 4. Greg wasn't married to Sara. 5. Each couple is represented by: Mr. and Mrs. Spade, the couple who plan to buy a new home, Paula and her husband, and Tom Heart. 6. Sam Spade wasn't married to Sara. |
| Torpe | Posted
on 22-Jan-03 10:38 PM
Noname, Yo bhucchuk tehaa bhaa bhaye tyo dubai guard laai sangai raakhera tyo RF ko Cap ko puzzle sodhyo; ani tini haru sochiraa belaa bhaagthyo... What is the answer anyway? Aaja raat bhari nidraa laagdaina yaar aba :) |
| arch119 | Posted
on 22-Jan-03 11:15 PM
the couples and their resolutions - 1) Tom Heart and Sara Heart (will take their kids to camping) 2) Mark club and Paula Club (planning to exercise at least twice a week) 3) Sam Spade and Martha Spade (not planning to buy a home -- Not sure about this one!!) 4) Greg Diamond and Carol Diamond (planning to buy new home) |
| nepalithhito | Posted
on 23-Jan-03 12:35 AM
the answer to bee is 175 miles. you have to think about the reletive velocity too. answer to the couple question 1) Tom Heart and Sara Heart 2) Mark club and Paula Club 3) Sam Spade and Martha Spade 4) Greg Diamond and Carol Diamond logic male names tom heart and sam spade given. greg is not mr club so mark is mr club and greg is mr diamond married to carol diamond. other couples sam is not married to sara and paula is not mrs spade so sam is married to martha paula is not mrs tom heart so is she is married to mark where as tom is married to sara. |
| arch119 | Posted
on 23-Jan-03 01:26 AM
Hi NepaliThito bro, Do you really think we have to consider the relative velocity in the "Bee vs. Trains Problem"? 'coz the person who stated the question seems to be well outside both of the trains. And anyway, we dont know the velocity of his frame of reference .So there is no question of relative velocity (relativity has no meaning without an observer). |
| Robert Frost | Posted
on 23-Jan-03 01:44 AM
arch119, I like you logic on the Hat one. It was really great. On the bee problem, I dont think relative velocity comes into equation and I dont think the answer is 175 too Nepalithito. I haven't solved it, but I got, (25+12.5+6.25+3.125+.......) so on......I didn't wanted to calculate it. |
| Robert Frost | Posted
on 23-Jan-03 01:54 AM
Here is another one: On Diplomat Row, a suburb of Washington DC, there are five houses. Each owner is a different nationality, each has different pet, each has a different favorite food, different favorite drink, and each house is painted a different color. 1. The green house is directly to the right of the Ivory house. 2. The Senegalese has the red house. 3. The dog belongs to the Spaniard. 4. The Afghan drinks tea. 5. The person who eats cheese lives next door to the fox. 6. The Japanese eats fish. 7. Milk is drunk in the middle house. 8. Apples are eaten in the house next to the horse. 9. Ale is drunk in the green house. 10. The Norwegian lives in the first house. 11. The perch eater drinks whiskey. 12. Apples are eaten in the yellow house. 13. The banana eater owns a snail. 14. The Norwegian lives next door to the blue house. For each house find (a) The color (b) The nationality of the occupant (c) The owner's favorite food (d) The owner's favorite drink (e) The owner's pet (f) Does the Zebra owner prefer vodka or ale? EINTEIN'S PUZZLE take time to solve it. Lets crack em up together, fellas!! |
| arch119 | Posted
on 23-Jan-03 02:57 AM
NO.1 NO.2 NO.3 NO.4 NO.5 Nation Norway Afhanistan Senegal Spain Japan Pet fox horse snail Dog Zebra Food apple cheese banana perch fish Drink vodka tea milk whiskey ale Color yellow blue red ivory green This solution satisfies all 14 conditions above but not sure whether the solution is unique coz there are only 14 constraints but (15+epsilon ) unknowns [the positions(15) + the relative positions of houses (epsilon) ] |
| arch119 | Posted
on 23-Jan-03 03:02 AM
Solution to the diplomat problem the view of my last post looks much different than I expected. So here i go once again , (1) is the leftmost ,(5) is the right most house (1) (Norway, Fox, Apple, Vodka, Yellow) (2) (Afghanistan,horse,cheese, tea, blue) (3) (Senegal, snail, banana, milk, red) (4) (Spain, dog, perch, whiskey, ivory) (5) (japanese,zebra,fish,ale,green) |
| Robert Frost | Posted
on 23-Jan-03 03:13 AM
arch119, did you solve the bee problem??? |
| arch119 | Posted
on 23-Jan-03 03:39 AM
nah man, thought i had done some problem like this while in school....... |
| thaag | Posted
on 23-Jan-03 02:40 PM
Bee travled 75 Miles |
| thaag | Posted
on 23-Jan-03 02:42 PM
Explanation of Bee Two trains travelling 100 miles apart at 50 MPH will take exactly 1 hour to collide. Bee is travelling at 75 Mph. So the bee will fly 75 miles in one hour |
| DWI | Posted
on 23-Jan-03 03:59 PM
I spent 25 minutes trying to see if Thaag explanation was right or wrong. Just use the velocity= distance * time formula. Then for each trip of the bee, the equation would be: 75/60 * T + 50/60 * T = 100 mile. Where 75/60 is the speed of the bee and 50/60 is the speed of the train. T is the time when the bee meets the other train first. From this equation T can be calculated and distance travelled by the bee in the first run is found. I found that the bee travels 60 miles and each trains travel 40 miles. In the second run, when the bee is coming back to the first train, the same equation can be used, with Right Hand Side = 20 mile. Where 20 mile is the distance left between the two trains. I found out that using this successive equations you get the answer almost equal to 75. I was ashamed to use 25 minutes to solve the problem that involves simple logic, and thus didn't post the answer. :) Did anybody solve noname's terrorist puzzle? Its a classic, try it out. I will leak the answer if nobody knows. Say what noname? |
| thaag | Posted
on 23-Jan-03 04:22 PM
No need to be asamed DWI, I used 35+ minutes to solve Diplomat question ;) |
| noname | Posted
on 23-Jan-03 04:24 PM
GREAT GOING guys! SAJHA ko lagi naya KHURAK!! Torpe don't give up hai....! DWI, it's really unfortunate that it was not brain-teasing for you! anyway, it's upto you to decide to let others know!! |
| DWI | Posted
on 23-Jan-03 04:31 PM
Noname, Did I say it wan't brain-teasing for me? no it wasn't me man. That one was classic problem, that's what I said. I just happen to know the answer beforehand as I had heard it before, should I answer it? Thaag, new one from you? |
| Robert Frost | Posted
on 23-Jan-03 06:55 PM
DWI and thaag, nice try guys :) definitely 10 out of 10 for that. I haven't solved the puzzle given by noname bro. I think now I definitely need the answer so DWI, would you please kindly releave this curios heart of mine otherwise like torpe said, Raat bhar needra lagdaina. We need some more puzzles here.... |
| DWI | Posted
on 23-Jan-03 07:35 PM
Noname's puzzle: The terrorists in rural side of Nepal are detaining you. There are only two doors in otherwise closed house. One of these, you know not which, leads to freedom and the other to execution. In front of each door there is a guard. All you know is that one of these guards always tells the truth and the other one always lies. Of course the guards know which door is which and which of them is a liar and which always tells the truth. You are permitted to ask one of the guards a simple yes/no question and then pass through the door of your choice. What question should you ask, that will guarantee that you can correctly choose the door to freedom? Robert Frost bro, here is a clue. It has to be a one sentence question (can be simple composites). Hint: You would have to involve both the guards in the question, directed towards only one. |
| Robert Frost | Posted
on 23-Jan-03 08:28 PM
sakiyena ba sakiyena...pakha ek chin....bhat khau ani sochaula... |
| Robert Frost | Posted
on 23-Jan-03 09:18 PM
DWI nice going on bee's problem though. This is what I got for my answer,(60+12+2.4+0.48+0.096+0.01792+0.002304+........)miles. Didn't wanted to calculate after that. Comes out close to 75 miles. I am still working on that noname's puzzle.... In the meantime, we need some more here.... |
| nepalithhito | Posted
on 23-Jan-03 09:31 PM
sorry i was wrong above. the answer is not 175 miles. but i do not think the answer is 75 miles either though it seems obvious answer. we are all forgetting that each time the bee leaves the train its velocity will be equal to its own velocity that it is travelling plus the velocity of the train so its actual velocity is 125 miles an hour so it will travel nearly 125 miles. if you use 125 as the velocity of the bee instead of 75, then you all will get the same answer. this is the answer if we do not consider the time lost in landing on the train and taking off again. thinking on noname problem too............ |
| nepalithhito | Posted
on 23-Jan-03 09:44 PM
new puzzle for all, three canibals and three professors arrive at the bank of the river. to cross the river there is a boat in which only two persons can ride at a time. if the number of canibals exceed the number of professor then the professor get eated. how many trips will it take to safely transport all 6 of them to another bank |
| DWI | Posted
on 23-Jan-03 10:46 PM
NepaliThhito, You are not applying the relative velocity properly. Observations aren't made from a conductor inside the train but us, outsiders. And for us the velocity is 50 and 60 in opposite direction (one will be negative of other). The answer has to be 75 miles. Use Thaag's simple logic or the one involving law of motion. About your question on the boat, nice one. I just gave it a thought and I can envision the transportation process to have 9 trips(counted eachway). Do you have a shorter method? |
| toilet paper | Posted
on 23-Jan-03 10:59 PM
For the Bee problem, What about the time the bee takes to make turn overs and change directions? This will definitely affect the time, and the velocity of the bee, as the final velocity will be zero (just before turning), and also the initial velocity will also be zero(right after turning). So now what's the right answer???? |
| nepalithhito | Posted
on 23-Jan-03 11:40 PM
toilet paper if you start thinking about all those things then, we will never be able to solve this problem because we are not provided with all the datas we are thinkning it as a hypothetical situation where the bee accelerates from 0 miles per hour to 75 miles per hour in 0 seconds. DWI it is not clearly stated in the problem if 75 miles per hour speed of bee is relative to earth or train. i was giving another scenario. any way i accept what you all have to say. now another interesting addition to the problem that i thought while thinking about that problem. how many times do you think bee can go from one train to another. let others also think about this boat problem. about no name's problem i think the question we have to ask is some thing like "ye sacho bolne dai, is this the door which leads to the freedom" but i am not sure if the liar will not respond to it. anyway thaks to DWI for the clue. |
| arch119 | Posted
on 24-Jan-03 12:22 AM
A few solutions to the terrorist problem 1) Go to whichever door you like and ask the guard " Is any one of the following sentences true ?- a)"U are a truthteller guarding the door leading to freedom" b)"U are a liar guarding the door leading to execution" " If he answers "Yes" go thru the door otherwise take the other one out. Proof - check with all 4 cases . Problem with this solution is that - this is "jabarjasti" tailored and contains one implicit "or" and two implicit "and"s and wont count as a "simple" Y/N question.So here is another one 2)Go to whichever door you like and ask the guard "Will the guard in the other door tell that THIS door leads to freedom(if I ask him) ?" if he answers "NO" take this door else switch your choice. proof:- case 1) if the guard u questioned is a truth-teller guarding the door leading to freedom (we will denote this here after by (truth-teller,freedom)), he will answer "No" for he knows that the other one is the liar and this door in fact leads to freedom. case 2) (liar,freedom) - the liar knows that the other one is truth teller and hence will say that this door leads to freedom .So he lies and says "no" case 3) (truth-teller,execution) - the truth teller knows that the other guard will lie and say that this door will lead to freedom.So he says yes case 4) (liar,execution) - the liar knows that the truth teller wont say that and he lies and says Yes. So sometimes , "no" saves your day. |
| arch119 | Posted
on 24-Jan-03 12:35 AM
P.S - thaag's solution to the "bee vs. train" problem is impressive. I will recommend " To Mock a Mockingbird and Other Logic Puzzles" by Raymond M. Smullyan and other books by the same author such as "Forever Undecided" and "Alice in puzzleland" for Logic-puzzle-hunters as well as Mathematics-fanatics. |
| arch119 | Posted
on 24-Jan-03 12:37 AM
The Infamous Monty Hall Problem The Setup you are presented with 3 doors (A, B, C) only one of which has something valuable to you behind it (the others are bogus) you do not know what is behind any of the doors You choose a door Monty then counters by showing you what is behind one of the other doors (which is a bogus prize), and asks you if you would like to stick with the door you have, or switch to the other unknown door The question is should you switch? Another question is Does it matter? |
| arch119 | Posted
on 24-Jan-03 08:46 AM
"Cannibal / Professor Problem" - It will take them 4.5 round-trips and this is how they shud do it - 1) A Cannibal and a Professor ride on the boat and cross the river. The Professor gets off at the opposite bank. 2)The Cannibal returns back and this time he and another Cannibal cross the river. 3) Next time the same Cannibal comes back and transports a professor....and so on. At the end of 4 roundtrips there will be 2 Professor and 2 Cannibals in the opposite bank & the Cannibal will have come back to transport the last Cannibal.They both cross the river in the final (0.5)th round-trip. Proof about the optimality - *to carry 6 in a boat which can accomodate only 2 ppl, we need at least 2.5 roundtrips but this is not possible coz the boat cant come back empty. *with 3.5 round trips , we can transport 8 ppl but but 3.5 round trips consists of 3 coming-backs . So 8 - 3 = 5 < 6 .So we cant transport 6 ppl in 3.5 round trips. *hence the next candidate is 4.5 round-trips......and its in fact possible for them to cross the river in 4.5 round-trips as shown above. |
| thaag | Posted
on 24-Jan-03 10:09 AM
Here is one by W.T. Pelletier Ten students, sitting in 2 rows of 5 each, took their 500-point final exam in advanced calculus. The students' scores were all multiples of ten with no two of them receiving the same score. Use the following clues and the professor's seating chart below to determine which students sat in which seats and the test score each student earned. 1) Hugh sat next to both Ida and to the student making 82%, which was the lowest grade on the test. 2) George and the student scoring 470 sat in diagonally opposite corner seats. 3) Chuck sat somewhere between Bill and the student scoring 410, although these 3 students are not necessarily in the same row. Similarly, Ann sat somewhere between Eve and the student scoring 490. 4) The sum of the scores of the students sitting in the first column is 880. 5) Jerry's score was 10 points better than Dolly's but 50 points less than Frank's. 6) The average score of those in Column 2 is the same as that of those in Column 4, but is 5 points less than the average of those in Column 3. 7) The student with the lowest score of those in the first row sat directly in front of the student with the highest score of those in the second row. 8) The average test score of those in the first row is 46 points higher than the average of those in the second row. |
| thaag | Posted
on 24-Jan-03 10:12 AM
Table: Column 1 Column 2 Column 3 Column 4 Column 5 ROW 2 Name 6. 7. 8. 9. 10. Score ROW 1 Name 1. 2. 3. 4. 5. Score PROFESSOR |
| thaag | Posted
on 24-Jan-03 10:15 AM
Table(ignore the dots) ....................Column 1...... Column 2 ........Column 3 .......Column 4....... Column 5 ROW 2....Name......6...............7...................8.................9...............10 ............Score . Row1.....Name.......1...............2...................3..................4................5 ...........Score .................................................Professor |
| thaag | Posted
on 24-Jan-03 10:29 AM
Football Problem Thaag and his 3 brothers(Chor, Daaka, Gunda) are big fans of the Washington Redskin football team, so they were thrilled to win tickets to watch the Redskin play for the NFL championship in the 2003 Superbowl. They wore their favorite jerseys, each a different color, to the game and sat together in 4 seats in a row. Each visited the concession stand during a different quarter of the game and bought a different snack from that of his brothers. determine the order in which they sat, the colors of their shirts, the quarter in which each bought his snack, and what snack each bought. 1) Daaka, the red-shirted one, the one who got a snack during the first quarter, and the one who bought a hot dog. 2)The fan who bought a snack during the 2nd quarter sat between the fans who bought popcorn and nachos. Gunda sat next to both the fan who bought a hot dog and the one who visited the concession stand in the first quarter. The green-shirted fan sat to the left of chor, who did not sit next to the popcorn muncher. The blue-shirted fan sat next to both the red-shirted and yellow-shirted fans. One boy got pizza in the 4th quarter. |
| thaag | Posted
on 24-Jan-03 11:13 AM
Switch / not switch solution A)Logically There is no point switching. Because, once he shows the bogus prize, it it 50% probability for any remaining door. B) But there is another side to it. if you choose door a ) that is 33% probability and after bogus door is shown, probability for the one you did not chhose door b & c is 66%. So if you change decision your probability becomes 66% rather than 33% Here is the catch.. if host knows he is showing bogus door then answer A) is correct if host doesn't know that he is showing bogus door then statically B) is correct |
| pasa | Posted
on 24-Jan-03 11:51 AM
Here is another interesting puzzle! There are Three lights in the first floor room. The lights are controlled by THREE switches in the basement. But it is not known yet which switch belongs to which light. You have to find Which Switch belongs to which light. You are allowed to go to the First floor only ONCE. (NOTE: You can not see lights from the basement.) Okay guys, try your best!!! --PASA-- |
| Logical Sense | Posted
on 24-Jan-03 01:44 PM
Pasa, this one is tough. Let me take a first crack on it. Since it does not say I could not much around with the switches downstairs, and simple solution would not work, you need to think logically (naturally...) 1) Put on one of the switch 2) Put off another switch. 3) Put a timer box in one of the swtiches and put it on for 3 minutes enough for you to climb upstairs to watch one of the light go off after 3 three minutes. So finally you know which one is which. Ha ha ha!!! I hope this is not the answer so that others can take a stab on it. - iti |
| SMSainju | Posted
on 24-Jan-03 01:49 PM
I think this is fairly straight forward.. turn one light on for almost 2-3 minutes. and then turn it off and then turn another one on and go upstairs. touch both off bulbs. SMSainju |
| Robert Frost | Posted
on 24-Jan-03 02:57 PM
pasa, nice puzzle, and the answer of both Logical sense and SMSainju looks perfectly good and logical to me. arch119 and thag bro, very nice problems!! |
| arch119 | Posted
on 24-Jan-03 06:13 PM
Solution to the monty hall problem - Thaag bro, The host (Monty) surely knows what is behind each door and will obviously open the door which contains the bogus prize .So after seeing a door which contains a "bogus" prize , our complete ignorance about whats behind each door decreases (i.e we get some "information" ,as C. Shannon would say) and hence its better to switch.. Here is a complete explanation http://www.geocities.com/arch119/answer.html |
| arch119 | Posted
on 24-Jan-03 09:44 PM
The"Football Problem" Unless I am misunderstanding something , the following 3 facts certainly lead to contradiction - Thaag bro, could u pls check the problem once again ? 1)The fan who bought a snack during the 2nd quarter sat between the fans who bought popcorn and nachos. 2)Gunda sat next to both the fan who bought a hot dog and the one who visited the concession stand in the first quarter. 3) One boy got pizza in the 4th quarter. |
| Robert Frost | Posted
on 25-Jan-03 08:29 PM
Comon fellas! we need more puzzles around this place? Mero brain chilayo puzzle solve garna napayera :) Lay it on!!!!!!!!!! |
| nepalithhito | Posted
on 25-Jan-03 08:46 PM
sorry to say but the solution to the boat problem is still not complete. i like the answer by arch119. quite simple and logical. but in the second trip when the canibal returns with another canibal, there are two canibals vs one professor in that bank so as the professor is outnumbered he will be eaten. lets think of this possibility too when we are solving boat problem. Robert Frost Bro hope this will be help your brain. also in the bee problem lets try to find out the number of times the bee will be able to travel from one train to another before they crash. |
| arch119 | Posted
on 25-Jan-03 09:43 PM
Sorry Nepalithhito bro, I think I had some misunderstanding with that boat problem....I was thinking that if only one of those two cannibals get out of the boat and one just comes back to the previous bank on the boat , then there will be just one cannibal and one professor in the bank. So even if the cannibal doesnt get off the boat, we should count him as being on the bank ,right ? |
| nepalithhito | Posted
on 25-Jan-03 10:28 PM
yes!! think we should be considering that too, other wise the puzzle becomes too simple. waiting for the corrected version fo Thaag's football problem and working on other. |
| arch119 | Posted
on 25-Jan-03 10:39 PM
Iin that case here is another solution - At any time , I will denote the condition of two banks symbolically, for example{ ( PPPCCC),()} means that there are 3 Prof.s and 3Cannies on the first bank while none in the another bank. Here is the procedure they shud follow - a) 1P and 1C (i will denote this by PC) goes to another bank condition = { (PPCC),(PC)} b) P gets back condition = { (PPPCC),(C)} c) CC go to another bank condition = { (PPP),(CCC)} d) C gets back and gets off condition = { (PPPC),(CC)} e) PP go to anohter bank condition = { (PC),(PPCC)} f) PC get back condition = { (PPCC),(PC)} g) PP go to another bank condition = { (CC),(PPPC)} h) C gets back condition = { (CCC),(PPP)} i) CC go to another bank condition = { (C),(PPPCC)} j) C gets back condition = { (CC),(PPPC)} k) CC go to another bank condition = { (),(PPPCCC)} So we need 5.5 round-trips. |
| arch119 | Posted
on 25-Jan-03 10:52 PM
Solution to lights and switch problem (in case the building is somewhere in NamcheBazaar - very cold!!! ) In this case the Bulb wont remain hot anymore .So we are in trouble . Here is what we can do , Turn on / off one of the switches continuously till we are sure the filament burns off ( ;) ) [ can guarantee that it will take less than 100 times if its made in nepal - thats why its Namchebazaar man] Then turn on another switch and go up to the room . So there are 3 bulbs in 3 states, one is working and on, another is working but off, and the third one has a molten filament (which we can easily confirm in case the bulb is trasparent , otherwise we will have to break 2 bulbs to confirm that). HOWZZAT !!! LOL |
| arch119 | Posted
on 26-Jan-03 08:59 AM
Seems like I am the noctornal creature here Anyway, here is my good morning to all sajhali-puzzle-hunters - "2 POTS Problem" Consider a silver and a golden pot, one of them containing a treasure. Assume that you can determine from the text prints which pot contains the treasure. The text prints on the pots are: The silver pot: "This pot is empty." The golden pot: "Exactly one of these texts is true." The Question: Which pot contains the treasure? |
| pasa | Posted
on 26-Jan-03 09:49 AM
Here you go Logical Sense jyu!!! You got a LOGICAL SENSE- 10 out of 10. SMSainju jee, Perfect answer. --pasa-- |
| Robert Frost | Posted
on 26-Jan-03 01:04 PM
Nepalithito bro, the number of times the bee will be able to travel from one train to another is I think something that comes out something like the following. here is what my answer was from previous attempts. (60+12+2.4+0.48+0.096+0.01792+0.002304+0.0004608+0.00009216+0.000018432.....) If I add the above it came out to 74.997624832. So I say its close to 75. I tried if I could come up with 75 just going on and on but it seems that it is not going to reach 75 miles until I add well, 100 times or what?? f* that man. 75 miles is the answer. |
| nepalithhito | Posted
on 26-Jan-03 07:24 PM
arch119 perfect answer. now answer to your problem. the treasure is hidden in silver pot. reason: if the inscription written in the golden pot is true then the inscription written in the silver pot is false so the treasure is hidden in the silver pot. if the incription written in the golden pot is false then that the inscription in the silver pot should also be false, so we know that the treasure is in silver pot. solution to bee problem, robert forst bro, since this is a hypothetical problem, the number of times that bee will have to travel to cover 75 miles is infinity. so could go on calculation for rest of your life but will get only 74.99999999999999999999999 but never exactly 75. try it if you want. |
| toilet paper | Posted
on 26-Jan-03 07:44 PM
OK, HERE IS ANOTHER ONE: Three birds are flying in a straight line. The bird in the front says," There are exactly two birds behind me." The one in the middle says," There is exactly one bird in front and one bird behind of me." Then the bird at the end says, "There are exactly two birds behind me." How can that be?????? |
| Torpe | Posted
on 26-Jan-03 07:59 PM
Toilet Paper (TP), The third bird must be facing in the opposite direction as the first two :) Torpe (TP). |
| toilet paper | Posted
on 26-Jan-03 08:32 PM
Almost there Torpe, but not quite. All three birds are facing the same direction. |
| arch119 | Posted
on 27-Jan-03 02:19 AM
Seems like the third bird is lying .... |
| arch119 | Posted
on 27-Jan-03 06:13 PM
Here is the nostalgic "where-did-the-1-Rupee-go?" puzzle which many people still find a mind-boggler - Scenario - 3 men go to a hotel , take one hotel room. They pay Rs. 30 ( each pay Rs 10) for the room. After some time the hotel attendant realizes that the actual rent of the room is Rs. 25. So he calls a maid , hands her Rs. 5 to give it back to those 3 men. She realizes that Rs. 5 will be difficult for those 3 to share among them.She keeps Rs.2 and gives them Rs.3 back. As a result,each of those 3 men pay Rs. 9 for the room. Question - 3 X 9 = 27 the maid has Rs. 2 27 + 2 = 29 Where did Re.1 go ??? |
| toilet paper | Posted
on 27-Jan-03 07:48 PM
Rs 30 - Rs 5 = Rs 25 Rs 25 + Rs 2 (The amount the maid took) = Rs 27 Rs 27 + Rs 3 (The amount the men got back) = Rs 30 OR Rs 30 + Rs 5 (The amount the attendant gave back) = Rs 35 Rs 35 - Rs 2 (The amount the maid took) = Rs 33 Rs 33 - Rs 3 (The amount the men got back) = Rs 30 |
| arch119 | Posted
on 28-Jan-03 07:00 AM
TP bro,The "Where-did-Re.1-go?" question, in fact , doesnt make any sense. Rs.27 is the amount spent by the 3 men. Rs. 2 is the money received by the maid. There is no reason why these two sum should add up to 30. The only thing that shud be true is the "principle of conservation of money" which is still true. ie money spent by 3 men = money received by the hotel person + money received by the maid ==> 27 = 25 +2 |
| Robert Frost | Posted
on 28-Jan-03 12:46 PM
TP bro, are the birds flying in a circle? I think its only possible if the birds are flying in a circle. But you have said straight line, so I think its impossible. Or is the third bird lying?? like arch bro said. K bho? bhanda, achamma bho! ha ha! Yo Re.1 kaha go bhanera khojda khojda ta jhandai mero raat bitya ha ha. You have already posted the answer. Yes, I think what TP bro came up with is good too. So, lets getting rolling with some more puzzles here. |
| Papra | Posted
on 28-Jan-03 01:59 PM
This is TOILET PAPER. Just writing under my friend's name. Hey Arch and RB, you guys got the answer for the bird problem. The third bird was a big time lier. It is like," An egg dropped from DharaHara, but did not break. What happened?" "Weird happened (Acchamma bho). Just wanted to add some humor to the thread. Hope you guys didn't waste much time trying to figure out the solution. |
| toilet paper | Posted
on 28-Jan-03 06:03 PM
Here is another one. There is a room 20 ft in lenght, 14 ft wide, and 15 ft tall. A detective 6 ft 2 inches, 185 lbs walks in the room and sees a man hanging by a rope, 3 ft tall and 1 inch in diameter on the celing. Apparently, the man had committed suicide. The detective looks around, and sees nothing the man could have used to standbut some water just benith the hanging man who is of course dead. Now the job for the detective is to find out how the man committed suicide since he did not see anything the man could have stood on and hung himself. |
| arch119 | Posted
on 01-Feb-03 07:52 AM
Recipe for a busy weekend - Wont let sajhapureans' grey cells rust .So here is another one A swimmer jumps from a bridge over a canal and swims 1 kilometer upstream. After that first kilometer, he passes a floating cork. He continues swimming for half an hour and then turns around and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant speed(relative to the river wild). The Question: How fast does the water in the canal flow? |
| arch119 | Posted
on 03-Feb-03 06:16 AM
K bho sajha - basi harulai ?? Was any Nepali Boka grazing here lately ?? If so , Welcome to the puzzle world !!! |
| TommyLii | Posted
on 03-Feb-03 05:44 PM
arch,I just want to confirm something.Can I suppose that the cork is at rest relative to the water ? |
| Robert Frost | Posted
on 03-Feb-03 11:58 PM
Welcome back from the weekend fellas!! Hope you guys had a terrific time. Now lets get going with our own puzzle mind, shall we?? There are some stunning puzzles by Arch bro. Lets solve it. |
| nepalithhito | Posted
on 04-Feb-03 01:13 AM
arch bro, yorosiku from nepali boka, any way found time to solve your second puzzle. the water in the can al flows at 1km/hr. |
| arch119 | Posted
on 04-Feb-03 01:52 AM
bull's eye . Nepalithito bro. |
| arch119 | Posted
on 04-Feb-03 01:53 AM
Yes , TommyLii you surely can. And My hello to Pamela Anderson Bhauju too. |
| arch119 | Posted
on 04-Feb-03 01:55 AM
P.S - (to TommyLii ) enjoyed watching your home video !!! LOL |
| thaag | Posted
on 05-Feb-03 01:06 PM
The Water in Chanal Flows .33 Km / hr |
| thaag | Posted
on 05-Feb-03 01:14 PM
correction swimmer's speed 2km /hr cork's speed=0.66km/hr |
| thaag | Posted
on 05-Feb-03 01:29 PM
Marble bag problem (I don't know if this is allowed) put 5 bags on each side of balance. 500gm vs 490gm take one marble out of 500gm side they should be equlal 490gm vs 490 gm take one marble out of any bag from 500 gm side and one marble from bag a of 490 gm side. if the scale balances, then repeat process but get marble from bag b of 490 gm side. When you hit the bag with 9 gm marbles. the balance will be heavier on the side of 490 gm marble and you will know which bag is the odd one |
| thaag | Posted
on 05-Feb-03 03:45 PM
711 solution 1.2, 1.25, 1.5, 3.16 |
| thaag | Posted
on 05-Feb-03 04:04 PM
Try fooling somebody with this one - 20 = - 20 -20 + 81/4 = -20 + 81/4 16 - 36 + 81/4 = 25 -45 + 81/4 (4)^2 - 2* 4 *(9/2) + (9/2)^2 = (5)^2 - 2*5*(9/2) +(9/2)^2 (4- 9/2)^2 = (5 - 9/5)^2 (4 - 9/2) = (5 - 9/2) 4=5 (How can it be possible) Of course if you don't follow rules |
| arch119 | Posted
on 05-Feb-03 05:42 PM
Thaag bro, The water and hence the cork both flow at 1 km/hr each...check ur calculations once again. About the marbles' problem ,first of all I would like to say that the weighing balance is not the one with two sides, its the one which can weigh stuffs accurately (with the "taraju"-like balance , the process will be more difficult.Anyway, how can u know which bag contains the marbles with 9 gms so that u can get marbles out of it ? -- Gambling ?) |
| arch119 | Posted
on 05-Feb-03 06:01 PM
About "the 4=5 Problem" Here is one more, 9 = 9 3 ^2 = (-3) ^2 3 = -3 You got the point, right ? There is no rule in mathematics which says that if x^2 = y^2 then x = y although it may seem trivial. What mathematics says (given x^2 and y^2 are both non-negative real numbers) is that, if x^2 = y^2 then either x=y or x=-y eg If (4- 9/2)^2 = (5 - 9/5)^2 then we cant say that (4 - 9/2) = (5 - 9/2) What we can say is , either (4 - 9/2) = (5 - 9/2) or (4 - 9/2) = - (5 - 9/2) In this case the second one holds. P.S- Generally, in these sort of problems ,usually, one of the following 2 things should have occur - a) There is division by zero (zero in its disguised form,of course) somewhere.. b) x = y is deduced from x^2 = y^2 coz these rules can easily deceive the mathematical intuition of a good deal of ppl. |
| arch119 | Posted
on 05-Feb-03 06:06 PM
P.S : Please post the process of solution coupled with the answer of the problem while doing so coz what we are interested in is not the answer but the way one solves the problem. I am sure we can learn from each others way of thinking and deduction. |
| thaag | Posted
on 05-Feb-03 09:55 PM
Arch bro no way the solution of the swimmer can be 1km /hr (if it is the way I understood). at constant speed swimmer swims 1km upstream. then releases cork which flows downstream. Swimmer continues to swim upstream for 1/2 hour. Then turns back downstream. Total swimming for swimmer 1km upstream+ 1/2 hr upstream + 1/2 hr downstream + 1 km downstream Total distance for cork 1 km If the speed of the cork is 1km /hr, the cork will reach the bridge at the time swimmer reaches the point where he initially release cork(one hour after reasing cork--remember 1/2hour upstream swim + 1/ hour downstream swim). But the swimmer still has to cover 1 km at the time cork reached bridge According to my understanding at the rate of 2km /hr swim Total time required by swimmer after releasing cork is 1/2 hour upstream + 1/2 hour down stream+1/2 hour(for 1 km at the speed of 2 km /hr) Total time after cork release = 1.5 hr distance to cover for cork = 1 km distancee=time*speed 1km=1.5hr* speed speed=0.66km/hr This problem can have multiple solution ;) |
| nepalithhito | Posted
on 05-Feb-03 11:32 PM
thag bro you are forgetting one important factor the speed of the water in the canal is going to affect the speed of swimmer. the swimmers speed is constant with respect to rivers wild so when he is swimming upstream his actual speed will be his speed - the speed of the river and when he is swimming downstream his actual speed will be his speed + the spped of the river. if you consider this factor you will find that the speed of the river is 1km/hr. the speed of the swimmer does not really matters. you have hit the bull eye with the 7-11 problem |
| arch119 | Posted
on 06-Feb-03 02:27 AM
Small note on "The river and the swimmer" problem - Here , if we try to analyze this problem from a 3rd persons perspective , then we have to do all those additions and substractions of the rivers velocity from that of the swimmer's. The best strategy here is to imagine yourself as being the cork ( Yes ! from right this moment, you are the cork floating on the river!!) .Now what u see around you is water( stagnant water !!! The same thing which is a river for an outsider is a lake for u now . See this is what Einstein was trying to say all the time !!! ). Now , its given that the swimmer is swimming with a constant velocity with respect to no body else in the world but YOU ("the cork"). Now imagine again , the swimmer starts swimming in the "lake" from the position where you are ...he swims for half an hour and then turns back and reaches u. So the total time between the moment he left you to the moment he met u again is 1 hour.(!!!) Now its time to see things from a 3rd persons point of view.(from right this moment on you are human again , not "the cork" ) YOu have known one thing - the time between the moment the swimmer left the cork and the moment he met the cork again is 1 hour. And being a 3rd person,you also know that the cork has travelled 1 km during this time (This is important !! If u are still imagining of urself being a cork , you will think that you are in rest and floating on the center of a big lake.See how dumb u were when u were a cork !!! Thats why its usually a good idea to see things from other ppls perspective ...you might find that there is something seriously wrong with u (philoshopical lecture -- you may ignore it!!) ) So , the cork travelled 1 km in 1hour and thus its velocity is 1km/hr ... HeHe wasnt that simple. Moral of the (loooong ) story - Always think things from the perspective of the thing or point or whatever with respect to which all the velocities are given. |
| nepalithhito | Posted
on 06-Feb-03 02:27 AM
By the thaag bro would you please look if there is any mistakes in the football problem that you posted earlier. the clauses you gave seems to contradict one another. |
| thaag | Posted
on 06-Feb-03 11:50 AM
I was wrong, I admit it...... Sorry thito for posting mistakes in football problem. i will try to post it correctly next time ;) |
| thaag | Posted
on 06-Feb-03 02:46 PM
Fill all _'s with appropriate number in this division problem _ _ 9 ) 6 _ 8 _ _ _ ( _ 5 3 _ _ _ 2 ------------- _ 9 _ _ _ _ 4 _ -------------- _ _ 4 _ _ _ _ _ --------------- 0 |
| thaag | Posted
on 06-Feb-03 02:47 PM
oops it did't come out in format |
| arch119 | Posted
on 06-Feb-03 05:58 PM
Here is the answer (will post the process later on , if required .Hint - Think simple !!! ) > 749 ) 638897(853 > 5992 > --------- > 3969 > 3745 > --------- > 2247 > 2247 > --------- > 0 |
| arch119 | Posted
on 06-Feb-03 06:00 PM
Why does Sajha eat all those spaces ?? |
| arch119 | Posted
on 08-Feb-03 02:55 AM
Answer to the Marbles problem- Number the bags from 1 to 10. From the bag with number x , take out x marbles. ( 1<=x<=10) .Accumulate all marbles and weigh them . Had all those marbles been 10 gms , the weight would have been 550 gm. but it will be (550 - k ) gms. (k > 0) This k is the number of the bag containing the the 9 gram marbles. |
| arch119 | Posted
on 09-Feb-03 06:51 AM
Test your logical and reasoning power. http://www.geocities.com/arch119/reynold.html |