This is the same problem as
Buckazoid Arithmetic II except that the four coins are one 1-buckazoid coin, one
2-buckazoid coin, one 3-buckazoid coin, and one 5-buckazoid coin. Once
again, of them is fake – it doesn’t weigh what it should – but you
don’t know whether it is heavier or lighter than a real coin. How can
you find the fake coin by using only a pan balance? You have no other
weights except for these four coins.