THE MOUSE-TRAP PUZZLE.
(
Combination and Group Problems)
[Illustration
6 20 2 19
13 21
7 5
3 18
17 8
15 11
14 16
1 9
10 4 12
]
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 ideal 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.
Answer:
If we interchange cards 6 and 13 and begin our count at 14, we may take
up all the twenty-one cards--that is, make twenty-one "catches"--in the
following order: 6, 8, 13, 2, 10, 1, 11, 4, 14, 3, 5, 7, 21, 12, 15, 20,
9, 16, 18, 17, 19. We may also exchange 10 and 14 and start at 16, or
exchange 6 and 8 and start at 19.
Informational
