long the other, "Four times
three are twelve;" while his tiny brother will count them all in rows,
"1, 2, 3, 4," etc. If the child's mother has occasion to add up the
numbers 1, 2, 3, up to 50, she will most probably make a long addition
sum of the fifty numbers; while her husband, more used to arithmetical
operations, will see at a glance that by joining the numbers at the
extremes there are 25 pairs of 51; therefore, 25x51=1,275. But his smart
son of twenty may go one better and say, "Why multiply by 25? Just add
two 0's to the 51 and divide by 4, and there you are!"

A tea merchant has five tin tea boxes of cubical shape, which he keeps on
his counter in a row, as shown in our illustration. Every box has a
picture on each of its six sides, so there are thirty pictures in all;
but one picture on No. 1 is repeated on No. 4, and two other pictures on
No. 4 are repeated on No. 3. There are, therefore, only twenty-seven
different pictures. The owner always keeps No. 1 at one end of the row,
and never allows Nos. 3 and 5 to be put side by side.

[Illustration]

The tradesman's customer, having obtained this information, thinks it a
good puzzle to work out in how many ways the boxes may be arranged on the
counter so that the order of the five pictures in front shall never be
twice alike. He found the making of the count a tough little nut. Can you
work out the answer without getting your brain into a tangle? Of course,
two similar pictures may be in a row, as it is all a question of their
order.

92.--_The Four Porkers._

The four pigs are so placed, each in a separate sty, that although every
one of the thirty-six sties is in a straight line (either horizontally,
vertically, or diagonally), with at least one of the pigs, yet no pig is
in line with another. In how many different ways may the four pigs be
placed to fulfil these conditions? If you turn this page round you get
three more arrangements, and if you turn it round in front of a mirror
you get four more. These are not to be counted as different arrangements.

[Illustration]

93.--_The Number Blocks._

The children in the illustration have found that a large number of very
interesting and instructive puzzles may be made out of number blocks;
that is, blocks bearing the ten digits or Arabic figures--1, 2, 3, 4, 5,
6, 7, 8, 9, and 0. The particular puzzle that they have been amusing
themselves with is to divide the blocks into two groups of five, a