Geometry
posted by John on .
How many ordered triples (a, b, c) of positive integers are there which satisfy the equation a + b + c = 10 ?

if a=1, b+c=9, so 8 there
if a=2, b+c=8. so 7 there
...
if a=8, b+c=2, so 1 there
Looks like 1+2+...+8 = 36
If no duplicates are allowed, the number goes way down.