144 Combinatorial & Topological Problemsmust contain nine of each figure 1, 2, 3, 4, and that they must be four-square
numbers without fractions or trick of any kind.- PROGRESSIVE SQUARES
This is a magic square, adding up 287 in every row, every column, and each
of the two diagonals. If we remove the outer margin of numbers we have an-
other square giving sums of 205. If we again remove the margin there is left a
magic square adding up 123. Now fill up the vacant spaces in the diagram with
such numbers from 1 to 81 inclusive as have not already been given, so that
there shall be formed a magic square adding up 369 in each oftwenty directions.20 5S :'0 (^57 28 71 26)
14 31 SO^29 60 35 68
58 46 3S 45 40 36 24
(^65 33 43 41 39 49 17)
(^64 48 42 37 44 34) IS
(^10 41 32 53 22 51 72)
56 27 52 25 54 11 62
- CONDITIONAL MAGIC SQUARE
Though there is nothing new to be said about the mere construction of a
perfect magic square, and the subject has a very large, though scattered,
literature of its own, a little variation that has some fresh condition is gener-
ally welcome. Here is a not difficult example.