Answer:
30
Explanation:
I can't prove this, but I can tell you the answer.
30.
a = 100 s digit
b = 10 s digit
5 is always the units digit.
I'm pretty sure that 30 is the correct answer.
What an interesting question. If I find out how it is done, I'll post it in the comments.
I can say this much.
a + b + 5 must be divisible by 3.
a = 1 b = 9 + 5
a = 1 b = 6 + 5
a = 1 b = 3 + 5
a = 1 b = 0 + 5
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Three more are obtained by interchanging the 100s and 10s digit except for b = 0
a = 9 b=1 + 5
a = 6 b =1 + 5
a = 3 b= 1 + 5
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a = 2 b = 2 + 5
a = 2 b = 5 + 5
a = 2 b = 8 + 5
only 2 more are obtained by interchanging the 10s and 100s digit
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a = 3 b = 4 +5
a = 3 b = 7 +5
You can't go any further. You get 2 more by interchanging the b and a digits.
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I hope you see what I've done here. I don't think this is an exact proof, but it is an exhaustive search.