In each of the three additions below, each letter represents a different digit; however, each letter does not necessarily represent the same digit in one addition as it does in another addition.
G A L E E L S A N E A L
+ N E A L + G A L E + E L S A
------------- ------------- -------------
E L S A N E A L G A L E
Which addition has the smallest sum?
This seems too simple to be the correct interpretation, but I found there were only seven cases which satisfied one of the three formulae (assuming that the leading digit for each word number was not zero):
Sum 1: 2165 + 3516 = 5681
Sum 1: 3165 + 2516 = 5681
Sum 3: 2615 + 6541 = 9156
Sum 3: 1725 + 7532 = 9257
Sum 2: 6135 + 2516 = 8651
Sum 1: 1725 + 3572 = 5297
Sum 1: 3725 + 1572 = 5297
Since 5297 is the smallest sum, it leads to the answer that the first addition (GALE + NEAL = ELSA) has the smallest sum (in two different assignments). Where's the perplexity?
Solution
