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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 realized by reference to the accompanying 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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