Consider three prime numbers A, B and C with A ≤ B ≤ C ≤ 20, and determine the total number of triplets (A, B, C) such that the respective last digits of A+B+C and A*B*C are the same. No computer programs!

The primes classified by ending digit:

1    11
2     2
3  3,13
5     5
7  7,17
9    19

The combinations of ending digits that lead to a match between the sum and the product end digits, with the number of ways of getting that combination of ending digits.

combination   quantity    sum/prod 
    123          2          6
    137          4          1
    159          1          5
    233          3          8
    235          2          0
    237          4          2
    239          2          4
    337          6          3
    357          4          5
    377          6          7
    379          4          9
    555          1          5
               ----
      total     39

Posted by Charlie on 2011-11-14 16:07:47