How many three digits numbers N=abc are there such that a≤b and c≤b?
Details and assumptions:
abc means 100a+10b+1c, as opposed to a×b×c. As an explicit example, for a=2,b=3,c=4, abc=234 and not 2×3×4=24.
The number 12=012 is a 2-digit number, not a three digit number.
I got the answer to be 328 but it says wrong. Solve it if you know hot to do it?
a=9: 999
a=8: 888 889 899
a=7: 777 778 779 788 789 799
a=6: 666 667 668 669 677 678 679 688 689 699
Looks like The number of entries for a=10-9 is the nth triangular number
Sum of 1st n triangular numbers is n(n+1)(n+2)/6
for n=9 that is 9*10*11/6 = 165