Mathematical_Recreations-Kraitchik-2e

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Mathematical Recreations
pegs on the board and removing all but the last by successive
moves.
For example, suppose that pegs are in just the six holes 35,
43,44,45,46,55. One can remove every peg but the center
one by the succession of moves: 45-65, 43-45, 35-55, 65-45,
46-44.
The most common problem is to start with all the pegs and
remove all but one. This problem is possible if and only if
the initially empty hole is one of the following: 24, 42, 46,
64; 34,43,45,54; 13, 15,31,37,51,57,73,75. In case the
problem is possible the last peg rests in one of the holes in
the list above.
Here is an extract from a letter of January 17, 1716, from
Leibnitz to Monmort:
" The game called Solitaire pleases me much. I take it in reverse
order. That is to say that instead of making a configuration
according to the rules of the game, which is to jump to an
empty place and remove the piece over which one has jumped, I
thought it was better to reconstruct what had been demolished,
by filling an empt.y hole over which one has leaped. In this way
one may set oneself the task of forming a given figure if that is
possible, as it certainly is if it can be destroyed. But why all
this?, you ask. I reply - to perfect the art of invention. For
we must have the means of constructing everything which is
found by the exercise of reason."
20. DOMINOES. Of all common games dominoes is certainly
one of the least standardized. To avoid misunderstanding
we give a set of rules which we shall assume
determine the basic game. *
There are 28 dominoes, running from 0-0 to 6-6. Two
players participate. When the whole set has been shuffled
face down on the table each player draws one to determine
who shall play first. The one with the higher total wins the
• The selection was quite arbitrary, dear reader. The rules by which
you play are doubtless just as good, perhaps better. - M. K.