mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

11 December

Noel has a large pile of cards. Half of them are red, the other half are black. Noel splits the cards into two piles: pile A and pile B.
Two thirds of the cards in pile A are red. Noel then moves 108 red cards from pile A to pile B. After this move, two thirds of the cards in pile B are red.
How many cards did Noel start with?
Note: There was a mistake in the original version of today's puzzle. The number 21 has been replaced with 108.

Show answer

5 December

Carol rolled a large handful of six-sided dice. The total of all the numbers Carol got was 521. After some calculating, Carol worked out that the probability that of her total being 521 was the same as the probability that her total being 200. How many dice did Carol roll?

Show answer

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024