mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Hat check

Three logicians, A, B and C, are wearing hats. Each has a strictly positive integer written on it. The number on one of the hats is the sum of the numbers on the other two.
The logicians say:
A: I don't know the number on my hat.
B: The number on my hat is 15.
Which numbers are on hats A and C?

Show hint


Show answer

Tags: logic
If you enjoyed this puzzle, check out Sunday Afternoon Maths LIV,
puzzles about logic, or a random puzzle.

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

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

Archive

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