258 Answers- THE NINE BARRELS
There are forty-two different arrangements. The positions of the I and 9 are
fixed. Always place the 2 beneath the 1. Then, if the 3 be beneath the 2 there
are five arrangements. If the 3 be to the right of the I there are five arrange-
ments with 4 under the 2, five with 5 under the 2, four with 6 under 2, two with
7 under 2. We have thus twenty-one arrangements in all. But the 2 might have
been always to the right of I, instead of beneath, and then we get twenty-one
reversed and reflected arrangements (practically similar), making forty-two
in all. Either the 4, 5, or 6 must always be in the center.
- THE EIGHT CARDS
You need only make the 8 and 9 change places, first turning the 9 round so
as to change it to a 6. Then each column will add up 18.- FIND THE NUMBERS
The two numbers composed of I's that sum and multiply alike are II and
1.1. In both cases the result is 12.1.141. MULTIPLYING THE NINE DIGITS
Dora was not to be caught by George's question. She, of course, immedi-
ately gave the correct answer, O. •- CURIOUS MULTIPLICAND
The number is 142,857. This is, of course, the recurring decimal fraction of
one-seventh.- ADDING THEIR CUBES
The required number is 153. The cubes of I, 5, and 3 are respectively
I, 125, and 27, and these added together make 153.
[Dudeney overlooked a fourth number: 371. Aside from I, these are the
only four numbers that are the sums of the cubes of their digits. For the more