Answer: 28
The winner is Alfie Wheeler of Glanrhyd, Cardigan, UK.
Worked solution
Since ENGLAND and GERMANY both contain A, E, G and N the first equation can be simplified to (LxNxD)/(RxMxY) = 1/4.
Since no other of the integers 1 to 9 is divisible by 5 or 7, two of A, E and G must have these values.
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The remaining integers when multiplied together give 9x8x6x4x3x2x1 = 34×27. Since (RxMxY) = 4(LxNxD), (RxMxYxLxNxD) is a number of the form 4×2. To produce a number of this form (34×27) must be divided by 8 (with x=18) or by 2 (with x=36).
If AxExG = 7x5x8, then LxNxD = 18 and RxMxY = 72:
either L, N, D are 9, 2, 1, and R, M, Y are 6, 4, 3;
or L, N, D are 6, 3, 1, and R, M, Y are 9, 4, 2.
If AxExG = 7x5x2, then LxNxD = 36 and RxMxY = 144:
L, N, D are 9, 4, 1, and R, M, Y are 8, 6, 3.
From the second equation (L+N+D)-(R+M÷Y) = -3:
if L, N, D are 9, 2, 1: (9+2+1) – (6+4+3) = -1;
if L, N, D are 6, 3, 1: (6+3+1) – (9+4+2) = -5;
if L, N, D are 9, 4, 1: (9+4+1) – (8+6+3) = 14 – 17 = -3 as required.
So A, E, G are (in any order) 7, 5, 2; L, N, D are (in any order) 9, 4, 1; R, M, Y are (in any order) 8, 6, 3.
So the sum of the letters of ANGLED is 28.
