mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Subsum

1) In a set of three integers, will there always be two integers whose sum is even?
2) How many integers must there be in a set so that there will always be three integers in the set whose sum is a multiple of 3?
3) How many integers must there be in a set so that there will always be four integers in the set whose sum is even?
4) How many integers must there be in a set so that there will always be three integers in the set whose sum is even?

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths LII,
puzzles about sums, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026