Response 0: A number is divisible by 3 if the sum of its digits is divisible by 3. In this case, the sum
of the digits of "ab5" must be divisible by 3, so a + b + 5 must be divisible by 3.
The smallest possible sum with a + b + 5 is 1 + 0 + 5 = 6, which is divisible by 3. The largest possible
sum is 9 + 7 + 5 = 21, which is also divisible by 3.
Therefore, the possible values of a + b can range from 1 to 16, with each increment of 3 leading to
another possible sum. There are 6 such increments (16 - 1) / 3 + 1 = 6, so there are 6 possible values
for a + b.
For each possible value of a + b, there are multiple combinations of digits that add up to that value.
For example, if a + b = 4, possible combinations are (1, 3), (2, 2), (3, 1) and (4 ,0).
Therefore, there are 30 different three-digit numbers that "ab5" can represent. (1 + 4 + 7 + 9 + 6 + 3
= 30)
In general, any three-digit number of the form "ab5" where a + b + 5 is divisible by 3 will be divisible
by 3.
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