Every letter a decimal digit, different letters for different digits:
BASE + BALL -------- GAMES
Which digit does each letter represent?
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Assuming numbers can't start with 0,
G is 1 because two four-digit numbers can't sum to 20000 or more.
If it is
LL must be a multiple of 9 because
ES are always congruent mod 9. But
LL is a multiple of 11, so it would have to be 99, which is impossible.
LL must be congruent to 100 mod 9. The only multiple of 11 that works is 55, so
L is 5.
1ES. This is possible when
S. The possibilities for
ES are 27, 38, or 49.
B must be at least 5 because
B (possibly +1 from a carry) is at least 10.
A is less than 5, then
A+1 does not carry, and
A must be even. Inversely, if
A is greater than 5, it must be odd. The possibilities for
A are 0, 2, 4, 7, or 9.
Mwould have to be 1.
Mwould have to be 5.
Mwould also have to be 9.
A is 4,
M is 9, and
B is 7. This leaves
38 as the only possibility for
ES. The full equation is:
7483 + 7455 -------- 14938
I found an answer by looking at the lowest numbers:
E + L must equal S or 10 + S S + L must equal E or 10 + E
I set L to zero which means that there won't be a one to carry. This allows me to set E = S ("es", not "five"). Let's pick a number:
E = 5 S = E = 5 L = 0
BA55 + BA00 ------ GAM55
Let's pick a number for A. This also gives us M. Note that if 2*A is < 10, A has to be even because it equals 2B - 10. If instead 2*A >= 10, the one carries over and A has to be odd because 2B + 1 - 10 has to equal A.
A = 2 M = 4
B255 + B200 ------ G2455
Now I see that B + B has to equal 12. B = 6:
6255 + 6200 ------ 12455
Using this method, I also found these results:
B = 7, A = 5, S = 5, L = 0, G = 1, E = 5, and M = 0 B = 8, A = 7, S = 1, L = 0, G = 1, E = 1, and M = 4
This method won't give every result because I'm assuming that L is always zero.