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THE EIGHTEEN DOMINOES.





(Magic Squares Problem.)
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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