mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths LII

 Posted on 2016-04-24 

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

More doubling cribbage

Source: Inspired by Math Puzzle of the Week blog
Brendan and Adam are playing lots more games of high stakes cribbage: whoever loses each game must double the other players money. For example, if Brendan has £3 and Adam has £4 then Brendan wins, they will have £6 and £1 respectively.
In each game, the player who has the least money wins.
Brendan and Adam notice that for some amounts of starting money, the games end with one player having all the money; but for other amounts, the games continue forever.
For which amounts of starting money will the games end with one player having all the money?

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about regular shapes, 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

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

Archive

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