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Archive for February, 2014

## Very full house

Posted by Chris under MathsChallenge (13 Responds)

A deck of cards is dealt to four players i.e. they get thirteen cards each.
What is the probability that exactly one of the players gets a complete suit?

## pqr

Posted by Chris under MathsChallenge (7 Responds)

If p, q and r are prime, and p divides qr − 1, q divides rp − 1, and r divides pq − 1, find all possible values of pqr

## Up the wooden hill

Posted by Chris under MathsChallenge (22 Responds)

If you can take 1, 2 or 3 steps at a time, how many different ways are there to climb 6 steps?
Don’t try for a general closed formula, it can be done, but it’s horrible. There is a nice generating function though.

## Girls, girls

Posted by Chris under Logic (15 Responds)

(Sorry, I couldn’t resist)
I was walking through the park when I bumped into an old acquaintance.
He told me that he had two children. What is the probability that he has two girls?
A girl joined us. He said it was one of his children. What is the probability that he has two girls?
He said she was [...]

## Boxed marbles

Posted by Chris under MathsChallenge (26 Responds)

You have three boxes and six marbles. If you randomly place the marbles in the boxes, what is the probability that you’ll place two marbles in each box?

## Points in a disc

Posted by Chris under MathsChallenge (2 Responds)

n points are selected on a circle. Every point is joined to the others by a line (a chord). What is the maximum number of intersections of the chords inside the circle and outside the circle?

## Average weight

Posted by Chris under MathsChallenge (5 Responds)

In a group of children and one adult there are b boys and g girls. If the average weight of the boys is g and the average weight of the girls is b, and the average weight of the whole group including the adult, whose weight is 42, is b + g. What is b [...]

## 444

Posted by Chris under Mathemagic (9 Responds)

Find all positive integers whose squares end with 444.
Show that no square can end with 4444.

## Dicey Dice 2

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

There are three fair dice, each numbered 1 through 6; one Blue, one Red, and one Yellow.
You and your opponent will each pick one die and roll. Highest number wins*.
*Special cases:
If there is a tie, and the values are EVEN: Blue beats Red, Red beats Yellow, and Yellow beats Blue.
If there is a tie, and [...]

## Dicey dice

Posted by Chris under Mathemagic (8 Responds)

You have three strangely numbered dice A: 3,3,5,5,7,7 B: 2,2,4,4,9,9 and C: 1,1,6,6,8,8
You are invited to gamble using any one of them. The winner is the one who rolls the highest number.
Should you pick your die first, or should you ask the challenger to pick his die first?

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