mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

Doubling cribbage

Brendan and Adam are playing 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.
Adam wins the first game then loses the second game. They then notice that they each have £180. How much did each player start with?

Show answer & extension

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

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

Archive

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