Bob’s Puzzle of the “Week”

Pool Ball Neighborhoods Solution

Labeling the balls with the letters ‘a’ through ‘o’, the neighborhood sums as ‘A’ through ‘O’, and the row sums as ‘W’ through ‘Z’ (from the top), we can solve using the equations below (which are easily verified geometrically).

A = 24
B = 43
C = 40
D = 41
E = 60
F = 50
G = 36
H = 62
I = 58
J = 45
K = 25
L = 32
M = 45
N = 44
O = 27

a = A - W
j = 8 (this was given)
g = (W + X + Y) - (E + j)
h = (Y + Z) - (K + N)
i = Y - (g + h + j)
d = (G + N) - (Y + Z)
f = (J + L) - (Y + Z)
e = X - (d + f)
k = (X + Y + Z) - (f + H + O)
o = (X + Y + Z) - (d + I + K)
l = (M + j + o) - (h + N)
n = (g + k + M) - (i + L)
m = (L + N) - (Y + Z)
b = (W + X + Y) - (D + f + i + j)
c = W - b

(the puzzle)

Back to Bob’s puzzle of the “week” page.