# Problem: The Mouse-trap Puzzle

This is a modern version, with a difference, of an old puzzle of the same name. Number twenty-one cards, $1, 2, 3,$ etc., up to $21,$ and place them in a circle in the particular order shown in the illustration. These cards represent mice. You start from any card, calling that card "one," and count, "one, two, three," etc., in a clockwise direction, and when your count agrees with the number on the card, you have made a "catch," and you remove the card. Then start at the next card, calling that "one," and try again to make another "catch." And so on. Supposing you start at 18, calling that card "one," your first "catch" will be $19.$ Remove $19$ and your next "catch" is $10.$ Remove $10$ and your next "catch" is $1.$ Remove the $1,$ and if you count up to $21$ (you must never go beyond), you cannot make another "catch."

Now, the idea is to "catch" all the twenty-one mice, but this is not here possible, and if it were it would merely require twenty-one different trials, at the most, to succeed. But the reader may make any two cards change places before he begins. Thus, you can change the $6$ with the $2,$ or the $7$ with the $11,$ or any other pair. This can be done in several ways so as to enable you to "catch" all the twenty-one mice if you then start at the right place. You may never pass over a "catch"; you must always remove the card and start afresh.

Solutions: 1

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### References

#### Project Gutenberg

1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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