August 2026 Problem of the Month

In the following multiplication problem, each letter represents a particular digit from 0 through 9 throughout.
Can you figure out the code?

Solution to the Problem:

Here is the solution:



T = 1
W = 6
O = 5
S = 9
I = 7
X = 2
L = 3
E = 0
A = 4
V = 8

Here is Seth Cohen's excellent explanation:

S and I can't be 1, because their products with TWO aren't TWO.   But I*O = O, and S*O = O (mod 10).   So O needs to be a number that has two multiples with itself in the ones digit.   The only digit that does this is 5, so O = 5.   So I and S are 3, 7, or 9.

(For O, I guess you could also look at the sum and see that L+O+O = L.   And since there can't be more than 1 carried from the previous sum, O+O = 10, so O = 5.)

X*5 = E, so E = 0, and X = 2, 4, 6, or 8.

I*TW5 = TT55.   If I = 3, T has to be at least 3 to make a four-digit answer, but then the answer is too big.   So I can't be 3.   Trying I = 7 and I = 9, with the options for W and T, you find that the only combo that works is I = 7, W = 6, and T = 1.

In the sum, L+5+5 = L, which will carry a 1.   So 1+V+the carried 1 = 0, so V = 8.

In the sum, L+5 = 8, so L = 3.   That leaves S = 9.

X*165 = 330, so X = 2, and we finish off with A = 4.