Alan and Bob have a whole number of dollars. Alan says to Bob, “If you give me $3, I will have n times as much as you”. Bob says to Alan, “If you give me $n, I will have 3 times as much as you”.

If n is a positive integer, what are its possible values?

This problem was originally posted by Karl Sharman (with a less idiotic title).

Whilst I was away under the pretence of work, a nearby bank uncovered a plot to swap the gold in their vaults with counterfeits. It was determined that all the gold bars in three of the Bank’s seven vaults were replaced with counterfeits. [...]

Would you take this bet?

Your friend he’s going to pick two different random numbers from a distribution not known to you. He will then write the two numbers of two small pieces of paper and put each one in each of his enclosed hands. You then pick a hand and he will reveal the [...]

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Maths
The prime 41, can be written as the sum of six consecutive primes:

41 = 2 + 3 + 5 + 7 + 11 + 13

This is the longest sum of consecutive primes that adds to a prime below one-hundred.

The longest sum of consecutive primes below one-thousand that adds to a prime, contains 21 terms, and [...]

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Maths
Suppose n fair 6-sided dice are rolled simultaneously. What is the expected value of the score on the highest valued die?

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Maths
Where the numbers 2n and 5n (where n is a positive integer) start with the same digit, what is the lowest possible value of n? The numbers are written in decimal notation, with no leading zeroes. I am going to get flak for this…. but, I have broad shoulders!

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Maths
With a standard pair of six sided dice, there is one way of obtaining a 2, two ways of obtaining a 3, and so on, up to one way of obtaining a 12. Find all other pairs of six-sided dice such that:

a. The set of dots on each die is not the standard {1,2,3,4,5,6}.

b. Each face has [...]

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Maths
Sue and Bob take turns rolling a fair 6-sided die. Once either person rolls a 6 the game is over. Sue rolls first, if she doesn’t roll a 6, Bob rolls the die, if he doesn’t roll a 6, Sue rolls again. They continue taking turns until one of them rolls a 6.

If Bob [...]