Upon receiving his student's card, Danny stated that he will never
forget its 5-digit number:
"It has only three distinct digits - one pair of equal digits followed by a pair of two other equal digits and the product of the second pair in the end.
Sum of the digits is over 30."

Is the above a sufficient mnemonic aid?

Yes.
If we call the number AABBC, we know immediately that B can only be 2 or 3.  If B=1, then C=1, but B can't be the same as C.

Is is possible for B=2?  If so, then the last number would be AA224, and A would have to be >11 in order for the SOD to be over 30.
So B=3 and the number is AA339.

For the SOD to be over 30, A must be >15/2.  Since C=9, A can only be 8.

Danny's number must be 88339.

Posted by Larry on 2018-01-20 08:17:47