Final answer:
To find Bart's house number, we must ensure it has a digit sum of 9, ends with a 1, and does not share any digits with the other two numbers. Given these constraints, the correct house number for Bart is 461.
Step-by-step explanation:
The question is a mathematical puzzle involving house numbers with three conditions: the sum of digits is the same for each house number, no number contains a digit in one of the other numbers, and no number begins with 4. Given that Bill's number is 252 and Ben's number begins with 6, we must determine Bart's house number with the information that it ends with a 1.
Since Bill's number is 252, the sum of his digits is 2+5+2, which equals 9. Ben's house number begins with a 6, so the remaining two digits must add up to 3, since none of the digits can be repeated in any of the numbers, and Bart's number cannot start with a 4 or any digits used in Bill's or Ben's numbers.
Bart's number must end with 1 and equal the same digit sum, 9; the only number that satisfies all the conditions is 461. Thus, among the options provided, Bart's house number is 461.