TAKE + HOME = EXAM

This is a cryptarithm.

Some solutions:

3875+1405=5280, T=3, A=8, K=7, E=5, H=1, O=4, M=0, X=2;

1875+3405=5280, T=1, A=8, K=7, E=5, H=3, O=4, M=0, X=2;

1325+4605=5930, T=1, A=3, K=2, E=5, H=4, O=6, M=0, X=9;

4325+1605=5930, T=4, A=3, K=2, E=5, H=1, O=6, M=0, X=9;

1985+3705=5690, T=1, A=9, K=8, E=5, H=3, O=7, M=0, X=6;

3985+1705=5690, T=3, A=9, K=8, E=5, H=1, O=7, M=0, X=6.

1076+5326=6402, T=1, A=0, K=7, E=6, H=5, O=3, M=2, X=4;

5076+1326=6402, T=5, A=0, K=7, E=6, H=1, O=3, M=2, X=4.

1306+5426=6732, T=1, A=3, K=0, E=6, H=5, O=4, M=2, X=7;

5306+1426=6732, T=5, A=3, K=0, E=6, H=1, O=4, M=2, X=7.

1057+6247=7304, T=1, A=0, K=5, E=7, H=6, O=2, M=4, X=3;

6057+1247=7304, T=6, A=0, K=5, E=7, H=1, O=2, M=4, X=3.

1057+6847=7904, T=1, A=0, K=5, E=7, H=6, O=8, M=4, X=9;

6057+1847=7904, T=6, A=0, K=5, E=7, H=1, O=8, M=4, X=9.

6387+1547=7934, T=6, A=3, K=8, E=7, H=1, O=5, M=4, X=9;

1387+6547=7934, T=1, A=3, K=8, E=7, H=6, O=5, M=4, X=9.

5617+2347=7964,  T=5, A=6, K=1, E=7, H=2, O=3, M=4, X=9;

2617+5347=7964,  T=2, A=6, K=1, E=7, H=5, O=3, M=4, X=9.

5837+1247=7084, T=5, A=8, K=3, E=7, H=1, O=2, M=4, X=0;

1837+5247=7084, T=1, A=8, K=3, E=7, H=5, O=2, M=4, X=0​.

There are more solutions.

There appear to be no solutions if we restrict the range of digits to 1-8.

The starting point is M, which must be an even number: 0, 2, 4, 6, 8. From this E could be 3, 4, 5, 6, 7, 8, 9.

by Top Rated User (639k points)