What number should go in the square marked X?
In the grid below, each of the blank squares and the square marked X are to be filled by the mean of the two numbers in its adjacent squares.
What number should go in the square marked X?
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Kindly provided by Alex Bellos Photograph: Whit Preston/Getty Images Three friends (A, B and C) are playing ping pong. They play the usual way: two play at a time, the winner stays on, and the loser waits his/her turn again. At the end of the day, they summarise the number of games that each of them played:
A played 10 B played 15 C played 17. Who lost the second game? Kindly provided by mycoted.com Shown above are four men buried up to their necks in the ground.
They cannot move, so they can only look forward. Between A and B is a brick wall which cannot be seen through. They all know that between them they are wearing four hatstwo black and two whitebut they do not know what colour they are wearing. Each of them know where the other three men are buried. In order to avoid being shot, one of them must call out to the executioner the colour of their hat. If they get it wrong, everyone will be shot. They are not allowed to talk to each other and have 10 minutes to fathom it out. After one minute, one of them calls out. Question: Which one of them calls out? Why is he 100% certain of the colour of his hat?
The factorial on n, written n!, is defined by n! = 1 x 2 x 3 x ... x (n2) x (n1) x n. For how many positive integer values of k less than 50 is it possible to find a value of n such that n! ends in exactly k zeros? Eight identical regular octagons are placed edge to edge in a ring in such a way that a symmetrical star is formed by the interior edges.
If each octagon has side length 1, what is the area of the star? Kindly provided by Øyvind Jakobsson A number is chosen from the grid above and you are asked to guess what the number is?
If your guess is too high then then your number, and all higher numbers in the grid, are removed. If your guess is too low then then your number, and all lower numbers in the grid, are removed. 1. How many attempts do you need to guarantee a correct result? 2. What is the expected number of attempts required for a correct answer? Kindly provided by Carl Vandal John lives on a remote island supplied by a ship.

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