Puzzle Types

CARD TRIANGLES.

(Problems Concerning Games.)
Here you pick out the nine cards, ace to nine of diamonds, and arrange
them in the form of a triangle, exactly as shown in the illustration, so
that the pips add up the same on the three sides. In the example given
it will be seen that they sum to 20 on each side, but the particular
number is of no importance so long as it is the same on all three sides.
The puzzle is to find out in just how many different ways this can be
done.
If you simply turn the cards round so that one of the other two sides is
nearest to you this will not count as different, for the order will be
the same. Also, if you make the 4, 9, 5 change places with the 7, 3, 8,
and at the same time exchange the 1 and the 6, it will not be different.
But if you only change the 1 and the 6 it will be different, because the
order round the triangle is not the same. This explanation will prevent
any doubt arising as to the conditions.


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