# Puzzles

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#### Sunday Afternoon Maths LIX

Turning SquaresElastic Numbers

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#### Sunday Afternoon Maths LVIII

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#### Advent Calendar 2016

#### Sunday Afternoon Maths LVII

Largest Odd FactorsList of All Puzzles

## Tags

time geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent arrows## The Sixth Cent

Source: Futility Closet

You toss 6 fair coins, and I toss 5 fair coins. What is the probability that you get more heads than I do?

## Marbles

Source: UKMT Senior Maths Challenge 2014

A bag contains \(m\) blue and \(n\) yellow marbles. One marble is selected at random from the bag and its colour is noted. It is then returned to the bag along with \(k\) other marbles of the same colour. A second marble is now selected at random from the bag. What is the probability that the second marble is blue?

## Fair Dice

Source: Futility Closet

Timothy and Urban are playing a game with two six-sided dice. The dice are unusual: Rather than bearing a number, each face is painted either red or blue.

The two take turns throwing the dice. Timothy wins if the two top faces are the same color, and Urban wins if they’re different. Their chances of winning are equal.

The first die has 5 red faces and 1 blue face. What are the colours on the second die?

## The Blue-Eyed Sisters

If you happen to meet two of the Jones sister (two sisters chosen at random from all the Jones sisters), it is exactly an even-money bet that both will be blue-eyed. What is your best guess of the total number of Jones sisters?

## Equal Opportunity

Source: Futility Closet

Can two (six-sided) dice be weighted so that the probability of each of the numbers 2, 3, ..., 12 is the same?

## Downing Street

A knot of spectators in Downing Street was watching members of the Cabinet as they arrived for a critical meeting.

"Who's that?" I asked my neighbour, as a silk-hatted figure, carrying rolled umbrella, rang the bell at No. 10. "Is it the Minister of Maths?"

"Yes," he said.

"Quite right," said a second spectator. "The Minister of Maths it is. Looks grim, doesn't he?"

The first of the speakers tells the truth three times out of four. The second tells the truth four times out of five.

What is the probability that the gentleman in question was in fact the Minister of Maths?