If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

AB + CD = 1CE, where AB and CD are two-digit numbers. The maximum sum of two two-digit numbers is 99+99=198, so 1CE is between 100 and 198, meaning the hundreds digit is 1. The sum is at least 100. Since AB + CD ≥ 100 and CD ≤ 99, we need AB ≥ 100 − CD. For the result to start with 1, there must be a carry. A appears in tens place of AB. The hundreds digit of result equals 1 (carry from tens place addition). For A to be uniquely determinable, A + C + (carry) = 10 + C (giving the C in result). So A + carry from units = 10, meaning A = 9 (with carry 1) or A = 10 (impossible). Hence A = 9.