MISCELLANEOUS PUZZLES
will make the number on the third car. That is, 78, 345, and
26,910 contain all the ten figures, and 78 multiplied by 345 makes
26,910. Now, the reader will be able to find many similar sets of
numbers of two, three and five figures respectively that have
the same peculiarity. But there is one set, and one only, in which
the numbers have this additional peculiarity—that the second
number is a multiple of the first. In other words, if 345 could
be divided by 78 without a remainder, the numbers on the cars
would themselves fulfil this extra condition. What are the three
numbers that we want ? Remember that they must have two,
three, and five figures respectively.
102.—
A Reversible Magic Square.
Can you construct a square of sixteen different numbers so that it
shall be magic (that is, adding up alike in the four rows, four columns
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