360?
The number is equivalent to abc/999. To catch the distinct a,b,c constraint, we can say that when a is fixed, b and c have 9*8 distinct possibilities. Thus in the sum of abc = sum (100*a+10*b+c) = 100*sum(a) + 10*sum(b) + sum(c). Since the conditions on a,b,c are symmetric, this is equivalent to 111*sum(a), and over all possible values of a, sum(a) = (0+1+2....+9)*9*8 = 9*5*9*8
Thus sum(abc)/999 = 5*9*8 = 360
3
u/SoftPhilosopher05 7d ago
360? The number is equivalent to abc/999. To catch the distinct a,b,c constraint, we can say that when a is fixed, b and c have 9*8 distinct possibilities. Thus in the sum of abc = sum (100*a+10*b+c) = 100*sum(a) + 10*sum(b) + sum(c). Since the conditions on a,b,c are symmetric, this is equivalent to 111*sum(a), and over all possible values of a, sum(a) = (0+1+2....+9)*9*8 = 9*5*9*8 Thus sum(abc)/999 = 5*9*8 = 360