on Thursday three times as many, and on Friday
twice as many. Urging the nuns to further efforts, she was pleased to
find on Saturday that an equal number slept on each of the four sides of
the house. What is the smallest number of nuns there could have been,
and how might they have arranged themselves on each of the six nights?
No room may ever be unoccupied.

[Illustration

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279.--THE BARRELS OF BALSAM.

A merchant of Bagdad had ten barrels of precious balsam for sale. They
were numbered, and were arranged in two rows, one on top of the other,
as shown in the picture. The smaller the number on the barrel, the
greater was its value. So that the best quality was numbered "1" and the
worst numbered "10," and all the other numbers of graduating values.
Now, the rule of Ahmed Assan, the merchant, was that he never put a
barrel either beneath or to the right of one of less value. The
arrangement shown is, of course, the simplest way of complying with this
condition. But there are many other ways--such, for example, as this:--

1 2 5 7 8
3 4 6 9 10

Here, again, no barrel has a smaller number than itself on its right or
beneath it. The puzzle is to discover in how many different ways the
merchant of Bagdad might have arranged his barrels in the two rows
without breaking his rule. Can you count the number of ways?

280.--BUILDING THE TETRAHEDRON.

I possess a tetrahedron, or triangular pyramid, formed of six sticks
glued together, as shown in the illustration. Can you count correctly
the number of different ways in which these six sticks might have been
stuck together so as to form the pyramid?

Some friends worked at it together one evening, each person providing
himself with six lucifer matches to aid his thoughts; but it was found
that no two results were the same. You see, if we remove one of the
sticks and turn it round the other way, that will be a different
pyramid. If we make two of the sticks change places the result will
again be different. But remember that every pyramid may be made to stand
on either of its four sides without being a different one. How many ways
are there altogether?

[Illustration]

281.--PAINTING A PYRAMID.

This pu