Substitute each letter by a different decimal digit from 0 to 9 to satisfy this alphametic division puzzle.
A N Y

I T S  I S L A N D
T N N A

T D U N
T L E N

S Y U D
S T N Y

S T I
Note: Derive a non computerassisted solution.
Given that A*S =
xA, N*S =
xN, and Y*S =
xS such that
x represents the 10
^{1}digit , S must be equal to 1 (thus, no 10
^{1}digit resulting in the product.
Only two products involving the multiplication of the distinct digits ITS with A, such that S = 1, will result in the pattern TNNA. These are where (A, I, T) = (9, 3, 2) and (4, 7, 2). Thus, T = 2; A = (4 or 9); and, correspondingly, I = (7 or 3).
With ITS * N and the deduced possible values of A, I and T and the value of S, the only value that results in the distinct digit pattern TLEN is 2568, with N = 8 and ITS = 321. Thus,
(A, E, I, L, N, S, T) = (4, 6, 3, 5, 8, 1, 2) or (9, 6, 3, 5, 8, 1, 2).
Now with the values known of more of the letter represented digits, the only value possible for 321 * Y is where Y = 4, resulting in the product 1284. Thus, as each letter represents a distinct digit, A = 9 and
(1, 2, 3, 4, 5, 6, 8, 9) = (S, T, I, Y, L, E, N, A).
ISLA  TNNA = 3159 – 2889 = 270 = TDU.
Therefore, D = 7 and U = 0.
Thus, (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) = (U, S, T, I, Y, L, E, D, N, A)
9 8 4

3 2 1  3 1 5 9 8 7
2 8 8 9

2 7 0 8
2 5 6 8

1 4 0 7
1 2 8 4

1 2 3

Posted by Dej Mar
on 20081119 10:00:23 