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Odd One
Which of the following objects below is the odd one?
SOLUTION
The second square is the odd one – each of the others has some unique feature (shape, boundary, color, size), except for it.
Category: Puzzles
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Reverse Puzzling
George is a great puzzler, so I was extremely surprised when he didn’t immediately know the answer to a really famous puzzle. It’s a puzzle that you probably did years ago, and have heard so often you can do it from memory rather than working it out. It’s also not really that difficult, so I was also surprised when it appeared to be stumping him.
“Come on, surely you know this one,” I said.
“I don’t. And don’t call me Shirley.” He answered grumpily. I could tell his mood was declining rapidly, but like any great puzzler he was down and not out, and I watched his facial expression change as he reached into his mental bag of tricks. He nodded towards a conveniently located whiteboard. “Have you got a marker for that?”
I handed him one, and he drew up the following diagram:
He stepped back, admiring his work, beaming proudly. “Well, now the solution is very obvious!” he commented. And indeed it was. The question for you is:
What is the puzzle?
SOLUTION
The diagram represents the puzzle about the man, trying to cross the river with a fox (F), a chicken (C) and a sack of barley (B). He can carry at most one of them with himself in the boat, and he shouldn’t leave the chicken alone with the fox or with the barley on one side of the river. The red dots represent all admissable configurations and the lines between them all available moves.
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Athletics Competition
An athletics competition, organized periodically, rewards a medal to 79 winners, 47 runner-ups, and an indeterminate number of third places. If 50 cans of drink are served for refreshment, how many policemen are needed to keep order?
SOLUTION
The numbers are references to elements in the periodic table. 79 is the number of Gold, 47 is the number of Silver, 50 is the number of Tin, and Bronze is not in the periodic table. Since 29 is the number of Copper, it should be the correct answer.
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100 Hats and 1 Million Dollars
A challenge is given to 100 people. A hat will be placed on each of their heads, and each hat will have an integer between 1 and 100 written on it (numbers can repeat). Every person will be able to see the hats of the other 99, but not his own. After that, everyone will have to guess what is the number on their hat (without others hearing). If at least one person guesses correctly, they will be awarded 1 million dollars. What strategy should the people come up with in order to optimize their chance of winning?
SOLUTION
Label the people with numbers 1, 2, 3, … , 100. A strategy which ensures 100% success is the following:
Person X should sum the numbers on the hats of the other 99 people, then subtract the result from X, and take the residue modulo 100 of the answer (say “100” if the residue is 0).
This way if the sum of the numbers on all hats has residue R when divided by 100, then person R will guess correctly the number on his hat.
Yes, No, I Don’t Know
Your friend is thinking of a number among 1, 2, and 3. You can ask him just one question, to which he is allowed to answer only with “yes”, “no”, or “I don’t know”. What would you ask him in order to find his number?
SOLUTION
You can ask him the following:
“If I am thinking of a number among 1 and 2, is your number going to be bigger than mine?”
If your friend’s number is 1, he will say “no”. If his number is 2, he will say “I don’t know”. If his number is 3, he will say “yes”.
Riddle of the Sphynx
Which creature walks on four legs in the morning, two legs in the afternoon, and three legs in the evening?
SOLUTION
Man – four limbs as a toddler, two feet as an adult, two feet and a walking stick as an elderly.
Puzzle Sum 18
What two American cities do these puzzle sums represent?
SOLUTION
NEST + ONE – STONE + WHEEL – HEEL + ARK = NEWARK
WHEEL + PIE + RING – PIER = WHEELING
MLN
This puzzle/game is played with groups of people, in which at least one of the participants knows the meaning of “MLN”, and the others are trying to figure it out.
All players must sit in a circle, facing each other. Then the people, who do not know what “MLN” stands for, take turns to ask questions. Every question must start with “Is MLN…” and must have a “yes” or “no” answer. Then a player who knows the meaning of “MLN” answers the question and the game continues until everyone solves the puzzle.
To play this game with your friends, at least one of you must know about the solution, which is explained below. Just keep in mind that whoever reads it, will lose the enjoyment of figuring it out by himself.
SOLUTION
The abbreviation “MLN” stands for “My Left Neighbor”. For example, if someone asks “Is MLN a boy?”, the answer will depend on the gender of the person on their left side. This makes the game both interesting and confusing.
68 Coins, 100 Weighings
You have 68 coins with different weights. How can you find both the lightest and the heaviest coins with 100 scale weighings?
SOLUTION
1. Compare the coins in pairs and separate the light ones in one group and the heavy ones in another. (34 weighings)
2. Find the lightest coin in the first group of 34 coins. (33 weighings)
3. Find the heaviest coin in the second group of 34 coins. (33 weighings)
Bridge Over the River
Pinkbird is trying to get to Redbird across the river. Where should we place the bridge, so that the path between the two birds becomes as short as possible?
Remark: The bridge is exactly as long as the river is wide, and must be placed straight across it. Additionally, it has some positive width.
SOLUTION
Notice that no matter how the bridge gets placed over the river, the shortest path would be to go to its top left corner, then traverse it diagonally, then go from its bottom right corner to Redbird. The second part of the way has fixed length, so we must minimize the first part plus the third part. In order to do that, imagine we place the bridge, so that its top left corner is at the current position of Pinkbird – point A. If the bottom right corner ends up at point C, then we must connect C with the position of Redbird – point B, and wherever the line intersects the bottom shore – point D, that will be the best place for the bottom right corner of the bridge.
