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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

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