Cayley's mousetrap
Encyclopedia
Mousetrap is the name of a game introduced by the English
mathematician
Arthur Cayley
. In the game, cards numbered one through
are placed in some random permutation
. Then, starting with the left-most card, the player begins counting "1, 2, 3, ...", moving to the next card as they increment their count. If at any point the player's current count matches the number on the card currently being pointed to, that card is removed, and the player starts over at one on the next card. When the player reaches the end of the cards (the right-most card), they simply wrap around to the left-most card and continue counting. If the player ever removes all of the cards from the permutation in this manner, then the player wins. If the player reaches
and cards still remain, then the cards win.
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Arthur Cayley
Arthur Cayley
Arthur Cayley F.R.S. was a British mathematician. He helped found the modern British school of pure mathematics....
. In the game, cards numbered one through
are placed in some random permutationPermutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
. Then, starting with the left-most card, the player begins counting "1, 2, 3, ...", moving to the next card as they increment their count. If at any point the player's current count matches the number on the card currently being pointed to, that card is removed, and the player starts over at one on the next card. When the player reaches the end of the cards (the right-most card), they simply wrap around to the left-most card and continue counting. If the player ever removes all of the cards from the permutation in this manner, then the player wins. If the player reaches
and cards still remain, then the cards win.