All Billy needs to do is to split the coins into two piles, one with 40 coins and one with 60 coins and then flip over all of the coins in the pile of 60. Note: if all of the heads-up coins are in the pile of 60 then both piles now contain zero heads. In general, for every tail in the pile of 60 there is a head in the pile of 40. If the pile of 60 contains x tails, then the pile of 40 contains the remaining (40-x) tails and x heads. When Billy flips all of the coins in the pile of 60, he turns the heads in that pile to tails, and tails to heads, so both piles will end up with exactly x heads.