Divide the set of integers from 1 to 15 into 2 subsets - a subset A of 13 numbers and B of 2 numbers so that the sum of the members of A equals the product of the two numbers in B.

For the set of positive integers 1 to N divided into two subsets A and B, such that A is the sum of N-2 of the elements and B is the product of the 2 elements not included in A, the solutions for subset B for N < 100 are:
10: B{6,7}
17: B{10,13}
26: B{15,21}
36: B{22,28}
37: B{21,31}
45: B{27,36}
50: B{28,43}
61: B{42,43}
65: B{36,57}
67: B{42,52}
78: B{45,66}
82: B{45,73}
91: B{52,78}
94: B{57,76}

Posted by Dej Mar on 2016-03-01 09:46:18