by Dudeney, Henry Ernest, 1857-1930
Available in 215 free installments
Owner:
example, it will be seen that the first and second magic squares given are of Type VI., that the third square is of Type III., and that the fourth is of Type I. Edouard Lucas indicated these types, but he dropped exactly half of them and did not attempt the classification.
typŁ
type h
?x
m
X
rype t\t
TYPE ^VT
E, T7II
TYPE
TYPE IX
TYPE.
type :xr
880
It is hardly necessary to say that everyone 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.
400.?THE MAGIC STRIPS.
1 2 3 4 5 6 7]
12 3 4 5 6/]
12 3 4 5 6 7
12 3 4 5 6 7
12 3 4 5 6 7
[12 3 4 5 6 7
12 3 4 5 6 7
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 maybe turned upside down or placed on their sides?that is, all the strips must lie in their original p 9 122 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.
401 .?EIGHT JOLLY GAOL BIRDS.
The illustration shows the plan of a prison of nine cells all communicating with one another by doorways. The eight prisoners have their numbers on their backs, and any one of them is allowed to exercise himself in whichever cell may happen to be vacant, subject to the rule that at no time shall two prisoners be in the same cell. The merry monarch in whose dominions the prison was situated offered them special comforts one Christmas Eve if, without breaking that rule, they could so place themselves that their numbers should form a magic square.
Now, prisoner No. 7 happened to know a good deal about magic squares, so he worked out a scheme and naturally selected the method that was most expeditious?that is, one involving the fewest possible moves from cell to cell. But one man was a surly, obstinate fellow (quite unfit for the society of his jovial companions), and he refused to move out of his cell or take any part in the proceedings. But No. 7 was quite equal to the emergency, and found that he could still do what was required in the fewest possible moves without troubling the brute to leave his cell. The puzzle is to show how he did it and, incidentally, to discover which prisoner was so stupidly obstinate. Can you find the fellow?
402.?NINE JOLLY GAOL BIRDS.
