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

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

Archive

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