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 numbers, 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

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

Archive

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