SOLUTIONS
3.—The Millers Puzzle.
The way to arrange the sacks of flour is as follows :—2, 78, 156,
39, 4. Here each pair when multiplied by its single neighbour makes
the number in the middle, and only five of the sacks need be moved.
There are just three other ways in which they might have been
arranged (counting the reversals as different, of course), but they all
require the moving of more sacks.
4.—
The Knight's Puzzle.
The Knight declared that as many as 575 squares could be marked
off on his shield, with a rose at every corner. How this result is
achieved may be realised
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by reference to the ac-
companying diagram:—
Join A, B, C, and D,
and there are 66 squares
of this size to be formed;
the size A, E, F, G,
gives 48; A, H, I, J,
32;
B.K.L,
M, 19;
B,N,O.P, 10; B,Q,
R, S, 4; E, T, F, C,
57; I, U, V, P, 33 ;
H,W,X,J,15; K.Y,
Z, M, 3 ; E, a, b, D,
82 ; H, d, M, D, 56 ;
H, e, f, G, 42 ; K, g,
f, C, 32; N, h, z, F, 24; K, h, m, b, 14; K, O, S, D, 16;
K, n, p, G, 10 ; K, q, r, J, 6 ; Q, t, p, C, 4 ; Q, u, r, i, 2. The
total number is thus 575. These groups have been treated as
if each of them represented a different sized square. This is
correct with the one exception that the squares of the form
B, N, O, P, are exactly the same size as those of the form
K, h, m, b.
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