NASIK (Type I.) . . . . . 48
SEMI-NASIK (Type II., Transpositions
of Nasik) . 48
" (Type III., Associated) 48
" (Type IV.) . . . 96
" (Type V.) . . . 96 192
___
" (Type VI.) . . . 96 384
___
SIMPLE. (Type VI.) . . . 208
" (Type VII.) . . . 56
" (Type VIII.). . . 56
" (Type IX.) . . . 56
" (Type X.) . . . 56 224
___
" (Type XI.) . . . 8
" (Type XII.) . . . 8 16 448
___ ___ ___
880
___

It is hardly necessary to say that every one of these squares will produce seven others by mere reversals and reflections, which we do not count as different.  So that there are 7,040 squares of this order, 880 of which are fundamentally different.

An infinite variety of puzzles may be made introducing new conditions into the magic square.  In The Canterbury Puzzles I have given examples of such squares with coins, with postage stamps, with cutting-out conditions, and other tricks.  I will now give a few variants involving further novel conditions.

399.—­THE TROUBLESOME EIGHT.

Nearly everybody knows that a “magic square” is an arrangement of numbers in the form of a square so that every row, every column, and each of the two long diagonals adds up alike.  For example, you would find little difficulty in merely placing a different number in each of the nine cells in the illustration so that the rows, columns, and diagonals shall all add up 15.  And at your first attempt you will probably find that you have an 8 in one of the corners.  The puzzle is to construct the magic square, under the same conditions, with the 8 in the position shown.

[Illustration]

400.—­THE MAGIC STRIPS.

[Illustration]

I happened to have lying on my table a number of strips of cardboard, with numbers printed on them from 1 upwards in numerical order.  The idea suddenly came to me, as ideas have a way of unexpectedly coming, to make a little puzzle of this.  I wonder whether many readers will arrive at the same solution that I did.

Take seven strips of cardboard and lay them together as above.  Then write on each of them the numbers 1, 2, 3, 4, 5, 6, 7, as shown, so that the numbers shall form seven rows and seven columns.

Now, the puzzle is to cut these strips into the fewest possible pieces so that they may be placed together and form a magic square, the seven rows, seven columns, and two diagonals adding up the same number.  No figures may be turned upside down or placed on their sides—­that is, all the strips must lie in their original direction.

Of course you could cut each strip into seven separate pieces, each piece containing a number, and the puzzle would then be very easy, but I need hardly say that forty-nine pieces is a long way from being the fewest possible.