Mathematical_Recreations-Kraitchik-2e

Numerical Pastimes 93
others getting smaller and smaller up to the top. This is the
Tower of Brahma. Day and night unceasingly the priests
transfer the disks from one diamond needle to another according
to the fixed and immutable laws of Brahma, which
require that the priests on duty must not move more than
one disk at a time, and that no disk may be placed on a needle
which already holds a smaller disk. When the sixty-four
disks shall have been thus transferred from the needle on
which at the Creation God placed them to one of the other
needles, then towers, temple, and priests alike will crumble
into dust, and with a thunderclap the world will vanish.
If we suppose that the priests can make one transfer every
second, with never a mistake, they must work for 264 - 1 =
18,446,744,073,709,551,615 seconds, or more than 500,000
million years.
We can rest easy. The end of the world will not come tomorrow.
13. JOSEPHUS' PROBLEM
1. During the cruel wars between the Moors and the Venetians,
a Moorish ship was returning to Africa laden down with
booty and captives, the latter to be sold as slaves. During
its passage the ship encountered a severe storm, and the captain
ordered that half of the 30 captives be thrown overboard
to save the ship and the crew. To choose the victims supposedly
without favor, the 30 prisoners (of whom 15 were men
and 15 were women) were placed in a circle, and every 9th
person was thrown overboard. But the captain, a gallant
and wily man, placed the women so that all of them were
saved. What places did the women occupy?
The solution can easily be found empirically. The women
must occupy the places numbered 1, 2, 3, 4, 10, 11, 13, 14,
15,17,20,21,25,28,29.
Many similar questions can be solved in the same manner.