Algebra
posted by John .
Out on my street, there are a certain number of pigeons sitting on telephone poles. If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space to sit on. If there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on. How many pigeons were there?

If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space ....the number of pigeons is odd. And, numberpigions=numberpoles*2+1
TIf there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on...means 3*poles1=number pigeosn
Pig=2Poles+1
Pig=3Poles1
subtract equation 1 from 2
0=poles2 or poles=2
pigeons=5 
Pi=2Po+1,
Pi=3(Po+1)
after solving we get the result as
Pi=9
and
Po=4