How can you buy 30 birds for 30 coins if partridges cost 3 c

How can you buy 30 birds for 30 coins, if partridges cost 3 coins each, pidgeons 2 coins each, and sparrows 2 for 1 coin? You have to buy at least one of each type of bird.

Solution

30 birds for 30 coins

Partridges - p - cost 3 coins

Pidgeons   - g - 2 coins

sparrows   - s   - 1 coin

p+g+s = 30

and 3p+2g+s = 30

2p+g =0

This implies g =-2p but no of birds cannot be negative

if at all p = g =0

But there should be atleast one of each type

Hence no way is possible