Math (Algebra)
posted by Arnau .
How many ordered pairs of integers (x,y) are there that satisfy x+y ≤ 10?

160

from (0,10) to (0,10)  21
from (1,9) to (1,9)  19
from (2,8) to (2,8)  17
..
from (9,1) to (9,1)  3
and (10,0)  1
same thing on the left side, but we can't count the centre line twice, so
sum = 2(1+3+5+...19) + 21
there are 10 terms in the series
sum = 2(5)(first + last) + 21
= 10(20) + 21 = 221
or 2(1+3+5+..+21)  21
= 2(11/2)(1 + 21)  21 = 221
There are 221 such ordered pairs.