if turned round in front of a mirror, four other
arrangements. All eight must be counted.

[Illustration:

/\ /\ /\
|2 | |5 | |2 |

/\ /\
|5 | |5 |

/\ /\ /\
|2 | |5 | |2 |

+---+---+---+ +---+---+---+ +---+---+---+
| 1 | 6 | 2 | | 2 | 6 | 1 | | 1 | 6 | 2 |
+---+---+---+ +---+---+---+ +---+---+---+
| 6 | | 6 | | 6 | | 6 | | 4 | | 4 |
+---+---+---+ +---+---+---+ +---+---+---+
| 2 | 6 | 1 | | 1 | 6 | 2 | | 4 | 2 | 3 |
+---+---+---+ +---+---+---+ +---+---+---+
A B C

]

277.--COUNTER CROSSES.

All that we need for this puzzle is nine counters, numbered 1, 2, 3, 4,
5, 6, 7, 8, and 9. It will be seen that in the illustration A these are
arranged so as to form a Greek cross, while in the case of B they form a
Latin cross. In both cases the reader will find that the sum of the
numbers in the upright of the cross is the same as the sum of the
numbers in the horizontal arm. It is quite easy to hit on such an
arrangement by trial, but the problem is to discover in exactly how many
different ways it may be done in each case. Remember that reversals and
reflections do not count as different. That is to say, if you turn this
page round you get four arrangements of the Greek cross, and if you turn
it round again in front of a mirror you will get four more. But these
eight are all regarded as one and the same. Now, how many different ways
are there in each case?

[Illustration:

(1) (2)

(2) (4) (5) (1) (6) (7)

(3) (4) (9) (5) (6) (3)

(7) (8)

A (8) B (9)

]

278.--A DORMITORY PUZZLE.

In a certain convent there were eight large dormitories on one floor,
approached by a spiral staircase in the centre, as shown in our plan. On
an inspection one Monday by the abbess it was found that the south
aspect was so much preferred that six times as many nuns slept on the
south side as on each of the other three sides. She objected to this
overcrowding, and ordered that it should be reduced. On Tuesday she
found that five times as many slept on the south side as on each of the
other sides. Again she complained. On Wednesday she found four times as
many on the south side,