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You have a big bag of flour, two 5lbs weights, and an inaccurate balance scale. How can you measure exactly 10lbs of flour?
Put both weights on one side, then fill the other side with flour so that the scale balances out. Then remove the weights and replace them with flour so that the balance scale is balanced again. The amount of flour you put there is exactly 10lbs.
One person went to the store and bought groceries for $13.59 total. He paid with a $100 bill, took his change, and left the store. There was something special about this transaction. What is it?
The person paid with a $100 bill. The cashier returned him a $50 bill, a $20 bill, a $10 bill, a $5 bill, a $1 bill, a quarter, a dime, a nickel, and a cent. The transaction consisted of exactly one of each (frequently used) denominations.
What number corresponds to 1985?
0 0 0 0 – 4
1 7 5 2 – 0
1 8 7 9 – 3
2 0 6 1 – 2
3 1 4 1 – 0
4 0 9 6 – 3
7 7 7 7 – 0
9 9 7 3 – 2
1 9 8 5 – ???
The numbers on the right count the total number of “holes” in the digits on the left. “1”, “2”, “3”, “4”, “5” and “7” have 0 holes in them. “0”, “6” and “9” have 1 hole in them. “8” has 2 holes in it. Therefore, the corresponding number is 3.
While going to the town fair, Tristan met 5 clowns on his way. Each clown had 4 dogs, each dog had 2 cats and each cat had 2 mice. How many in total were going to the fair?
Only Tristan. He met the others on his way to the fair, so they were coming back from there.
You have to descend a 100-meter vertical cliff. However, you have only a 75-meter long rope and a knife with yourself. On the top of the cliff and halfway down – 50 meters above the ground, there are two big pins stuck in it. How can you get safely down to the ground?
First, you cut the rope at 25 meters and make a loop at the end of the short part. Then you pass the longer part through the loop so that you get a 50-meter long rope (the second 25 meters are doubled). You use this rope to descend to the pin and grab it. Then tie one of the ends of the 50-meter rope to the pin, pull the rest back through the loop and let it fall to the ground.
Add just one line to create a correct equality.
Add a line to the plus to transform it into a four.
Which number must be written in the place of the dots?
Remark: The missing number does not necessarily have 3 digits.
If you turn the paper around, the text will read:
… = 19969 + 68199
99106 = 18108 + 80998
Therefore, the missing number is 88168, which after 180 degrees rotation becomes 89188.
100 prisoners are given the following challenge: They will be taken to a room and will be arranged in a column, such that each of them faces the backs of the prisoners in front. After that, black and red hats will be placed on their heads, and the prisoners will be asked one at a time what is the color of their hat, starting from the one at the back of the column. If a prisoner guesses his color correctly, he is spared; if not – he is executed. If every prisoner can see only the hats of the prisoners in front of him in the line, what strategy should they come up with, so that their losses are minimized?
There is a strategy which ensures that 99 prisoners are spared and there is 50% chance that one of them is executed. Clearly, one can not do better.
The strategy is as follows: The first prisoner (at the back of the line) counts the number of black hats worn by the prisoners in front. If the number is odd, he says “BLACK”. If the number is even, he says “RED”. Then, the second prisoner counts the black hats in front of him, figures out the color of his own hat, and answers the question.The third prisoner sees the number of black hats in front of him and uses this information, along with what the second prisoner’s hat is, to determine the color of his own hat. The prisoners continue in the same manner until all 99 prisoners in the front guess their hat colors correctly. The chance for survival of the first prisoner is 50%.
A chess king starts on one cell of a chessboard and takes a non-intersecting tour, passing through each square once, and ending up on the initial square. Show that the king has made no more than 36 diagonal moves.
The king must visit the 28 perimeter squares in order; otherwise, he will create a portion of the board which is inaccessible for him. However, he can not travel from one square to a neighboring one using only diagonal moves. Therefore, he must make at least 28 horizontal/vertical moves and at most 64 – 28 = 36 diagonal moves.
A square has dropped on the ground and broken into ten pieces. Accidentally, an additional, eleventh piece has fallen among the others. Can you figure out which one it is?
The total number of the squares in all pieces is 70 = 8 * 8 + 6. Therefore the extra piece is the one consisted of 6 squares.
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