mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Turning squares

Each square on a chessboard contains an arrow point up, down, left or right. You start in the bottom left square. Every second you move one square in the direction shown by the arrow in your square. Just after you move, the arrow on the square you moved from rotates 90° clockwise. If an arrow would take you off the edge of the board, you stay in that square (the arrow will still rotate).
You win the game if you reach the top right square of the chessboard. Can I design a starting arrangement of arrows that will prevent you from winning?

Show answer

Placing plates

Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?

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

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

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

Archive

Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019