1. ## Decoding letters

Can anybody shed some light on this as how to solve it with equations:

T W O
X T W O
-------------
T H R E E

2. Originally Posted by nazz
Can anybody shed some light on this as how to solve it with equations:

T W O
X T W O
-------------
T H R E E
For a start, T must be 1 (because if you square a three-digit number starting with 2 or 3, then the square will be greater than 40000, which is too big; and if the first digit is 4 or more then the square will have six digits). Next, the only squares ending in a repeated digit must end in either 00 or 44. That narrows the possibilities down to very few, and you can check that the only solution is
Code:
    1 3 8
X 1 3 8
_________
1 9 0 4 4