mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Twenty-one

Scott and Virgil are playing a game. In the game the first player says 1, 2 or 3, then the next player can add 1, 2 or 3 to the number and so on. The player who is forced to say 21 or above loses. The first game went like so:
Scott: 3
Virgil: 4
Scott: 5
Virgil: 6
Scott: 9
Virgil: 12
Scott: 15
Virgil 17
Scott: 20
Virgil: 21
Virgil loses.
To give him a better chance of winning, Scott lets Virgil choose whether to go first or second in the next game. What should Virgil do?

Show answer & extension

Tags: numbers, games
If you enjoyed this puzzle, check out Sunday Afternoon Maths XXVI,
puzzles about games, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025