Let abcde be the number.
a+c = b <= 9
c+e = d+1 <= 10
a > 0
b and d are determined by c, a and e.
c = 0: 9 choices for a * 9 choices for e = 81 choices (1<=a<=9; 1<=e<=9)
c = 1: 8 choices for a * 10 choices for e = 80 choices (1<=a<=8; 0<=e<=9)
c = 2: 7 choices for a * 9 choices for e = 63 choices (1<=a<=7; 0<=e<=8)
c = 3: 6 choices for a * 8 choices for e = 48 choices etc.
c = 4: 5 choices for a * 7 choices for e = 35 choices
c = 5: 4 choices for a * 6 choices for e = 24 choices
c = 6: 3 choices for a * 5 choices for e = 15 choices
c = 7: 2 choices for a * 4 choices for e = 8 choices
c = 8: 1 choices for a * 3 choices for e = 3 choices
c = 9: 0 choices for a * 2 choices for e = 0 choices

357 such numbers abcde.
Edited on October 12, 2015, 3:30 pm

Posted by Charlie
on 20151012 15:29:02 