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# Cryptarithm

The Irish Times is a great supporter of Maths Week. We can express this in a cryptarithm as:

IRISH

+TIMES

= MATHS

In a cryptarithm the numbers in a sum are replaced by letters. Each letter represents a distinct digit, multiple occurrences of a letter refer to the same digit and the leftmost numbers cannot be zero. The challenge is to figure out what numbers the letters correspond to. Cryptarithms can take a lot of time and patience; they are usually solved by applying some logic and a lot of trial and error. To reduce the time demand I can tell you that R = 8 and E = 1

.   I  8 I S H

+ T I M 1 S

= MAT H S

On inspection of left hand side. S + H = S therefore H must be 0

.   I  8 I S  0

+ T I M 1 S

= MAT 0 S

If 1 + S = 0 then S must be 9

.   I  8 I 9  0

+ T I M 1 9

= MAT 0 9

1 + M + I = T  or possibly T + 10 (ie carry 1 across)

8 + I = A  or possibly 1+ 8 + I = A+ 10 as I not 1, 8 + I (+1) not 10

I + T = M ( I + T < 10 and cant be 9)

Working through like this and trying some speculative guesses eventually leads you to-

Solution I = 4, R = 8, S = 9, H = 0, T = 2, M = 7, E = 1, A = 3.

48490

+ 24719

= 73209 