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Amusements in Mathematics by Henry Ernest Dudeney
page 329 of 735 (44%)

405.--CARD MAGIC SQUARES.

[Illustration]

Take an ordinary pack of cards and throw out the twelve court cards.
Now, with nine of the remainder (different suits are of no consequence)
form the above magic square. It will be seen that the pips add up
fifteen in every row in every column, and in each of the two long
diagonals. The puzzle is with the remaining cards (without disturbing
this arrangement) to form three more such magic squares, so that each of
the four shall add up to a different sum. There will, of course, be four
cards in the reduced pack that will not be used. These four may be any
that you choose. It is not a difficult puzzle, but requires just a
little thought.


406.--THE EIGHTEEN DOMINOES.

The illustration shows eighteen dominoes arranged in the form of a
square so that the pips in every one of the six columns, six rows, and
two long diagonals add up 13. This is the smallest summation possible
with any selection of dominoes from an ordinary box of twenty-eight. The
greatest possible summation is 23, and a solution for this number may be
easily obtained by substituting for every number its complement to 6.
Thus for every blank substitute a 6, for every 1 a 5, for every 2 a 4,
for 3 a 3, for 4 a 2, for 5 a 1, and for 6 a blank. But the puzzle is to
make a selection of eighteen dominoes and arrange them (in exactly the
form shown) so that the summations shall be 18 in all the fourteen
directions mentioned.
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