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Posts under MathsChallenge

## Stacked Deck (part 4)

Posted by DP under Logic, Mathemagic, MathsChallenge, Tom (5 Responds)

Andy, Bob, Charlie, and Dave are ready to play another round of cards. This time it is Charlie’s turn to deal.
The cards are sorted and Charlie decides to only use the Red cards (Hearts & Diamonds).
Three [3] cards are dealt one-at-a-time to each of the four [4] players. Highest pair wins; Aces are low.
If no [...]

## A yes/no test

Posted by Chris under Logic, MathsChallenge (6 Responds)

In a test involving yes/no answers, the probability that the official answer is correct is t, the probability of getting the real correct answer is b for a boy and g for a girl. If the probability that a randomly chosen boy or girl of getting the official answer to a question is 1/2, then [...]

## It’s as easy as a, b, c

Posted by Chris under MathsChallenge (6 Responds)

Find all solutions in positive integers a, b, c to the equation
a! b! = a! + b! + c!

## 916238457

Posted by Chris under MathsChallenge (13 Responds)

916238457 is a nine-digit number that has the property that has the digits 1 to 9 exactly once and the digits 1 to 5 are in counting order but the digits 1 to 6 are not. How many such numbers are there?

## Golden Needle in a Haystack

Posted by DP under MathsChallenge (7 Responds)

I have a very large plot of land on which I have stacked bales of hay, each measuring 1m x 1m x 1m. They are stacked 10 bales high, and span a couple thousand wide and deep. To keep them out of the weather I have also placed a tarp on top that cannot be [...]

## Untwinned twins

Posted by Chris under MathsChallenge (2 Responds)

A class has six pairs of twins. The teacher wishes to set up teams for a quiz, but doesn’t want to put any pair of twins in the same team.
1) In how many ways can they be split into two teams of six?
2) In how many ways can they be split into three teams of [...]

## Alan and Bob’s cash

Posted by Chris under MathsChallenge (7 Responds)

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?

## The vexatious vault value veracity validation problem

Posted by Chris under Logic, Mathemagic, MathsChallenge (12 Responds)

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. [...]

## Another die rolling game

Posted by Chris under Logic, MathsChallenge (10 Responds)

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 [...]

## Alternating series

Posted by Chris under MathsChallenge (13 Responds)

An increasing sequence of integers is said to be alternating if it starts with an odd term, the second term is even, the third term is odd, the fourth is even, and so on. The empty sequence (with no term at all!) is considered to be alternating.
Let A(n) denote the number of alternating sequences which [...]

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