Not 99+99
Logic
Level
2
If each letter above represents a distinct digit, what's the maximum possible value of the summation?
167
176
183
198
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Becuase we want to use distinct digits throughout, observe that A B + C D = 1 0 ( A + C ) + ( B + D ) ≤ 1 0 × ( 9 + 8 ) + ( 7 + 6 ) = 1 8 3 .
If { A , C } = { 9 , 8 } , then the largest possible value of E F G where we use digits distinct from 8 and 9 would be 176. We can verify that this can be achieved, for example by 9 2 + 8 4 = 1 7 6 . (There are other solutions too. Can you find them?).
If { A , C } = { 9 , 8 } , then we will have A B + C D = 1 0 ( A + C ) + ( B + D ) ≤ 1 0 × ( 9 + 7 ) + ( 8 + 6 ) = 1 7 4 . As such, the largest possible value of E F G will be at most 174, which is smaller than the 176 that we calculated earlier.
Hence, the largest possible value of E F G is 176.