mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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?

Show answer & extension

The sixth cent

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

Show answer & extension

Marbles

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?

Show answer & extension

Fair dice

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?

Show answer & extension

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?

Show answer & extension

Equal opportunity

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

Show answer & extension

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?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020