TO + GO = OUT. Find the value of T + G + O + U?

Step 1: The sum of two two-digit numbers results in a three-digit number, so the hundreds digit of the result must be 1. This means O = 1.

Step 2: In the units place, O + O = T. Since O = 1, 1 + 1 = 2, so T = 2.

Step 3: In the tens place, T + G must produce a carry to the hundreds place, so T + G ≥ 10. With T = 2, G must be at least 8.

Step 4: If G = 8, then 2 + 8 = 10, so U = 0 and carry 1, which is valid. If G = 9, then 2 + 9 = 11, so U = 1, but O is already 1, so U cannot be 1. Thus, G = 8 and U = 0.

Step 5: T + G + O + U = 2 + 8 + 1 + 0 = 11.