# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

#### Sunday Afternoon Maths LXIV

Equal lengthsDigitless factor

Backwards fours

List of all puzzles

## Tags

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

Two points along a drinking straw are picked at random. The straw is then bent at these points. What is the probability that the two ends meet up to make a triangle?

## 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?