[Illustration]
The puzzle is to place a different number in each of the ten squares so
that the sum of the squares of any two adjacent numbers shall be equal
to the sum of the squares of the two numbers diametrically opposite to
them. The four numbers placed, as examples, must stand as they are. The
square of 16 is 256, and the square of 2 is 4. Add these together, and
the result is 260. Also--the square of 14 is 196, and the square of 8 is
64. These together also make 260. Now, in precisely the same way, B and
C should be equal to G and H (the sum will not necessarily be 260), A
and K to F and E, H and I to C and D, and so on, with any two adjoining
squares in the circle.
All you have to do is to fill in the remaining six numbers. Fractions
are not allowed, and I shall show that no number need contain more than
two figures.