Alphametics?

Question

An alphametic is a computation puzzle using letters instead of digits. Each letter represents one of the digits 0-9, and two different letters cannot represent the same digit. Some alphametic puzzles have more than one answer.

Find the value for each letter in each alphametic.

1. HALF + HALF = WHOLE

2. TWO + TWO = FOUR

Answer 1

Well, we know
1) E is an even number because 2*f = either E or 10+E
2) W is 1, because we "carried" the 1
3) H is at least 5
4) L+L=L (so L=0) or 2F=10+E, we carried the 1, so L+L ends in L-1, which is not possible. So L=0, and E is even, and F < 5 (so it is 2, 3, or 4
Suppose F = 2, then E = 4
and HA+HA=1HO. H has to equal 9 so that 1HO can be 19O
then A+A=10+O. What's left for A (and therefore O?) A cannot be 5 because then 2A=10 and zero is taken by L. A=6 doesn't work because F=2. A=7, then F=4 but E is 4. A=8 works, in which case O is 6!
Check our work:
9802 + 9802 = 19604
HALF+HALF = WHOLE

The same logic can be used to solve the second problem. God for the obviouis (F=1), and work toward the harder ones.