Puzzle of the Week for 22 February 1999

One morning, three pirates (whose names were Arrgh, Bluster, and Cruft) baked a batch of chocolate chip cookies and left them on a plate to cool off. Arrgh didn't trust Bluster or Cruft, so (when they weren't looking) he sneaked into the galley and divided the cookies into three equal shares. After dividing them, there was one cookie left, so he gave it to Squawwk, their one-eyed parrot. (The pirates' code of honor forbids breaking cookies when sharing them out.) Arrgh took his share of the cookies and put the other two shares back on the plate.

A few minutes later, Bluster, who didn't trust Arrgh or Cruft, crept into the galley for his share of the cookies. He divided them into three equal piles, gave the extra cookie to Squawwk, took one pile for himself, and returned the other two piles to the plate.

Cruft was no less suspicious of Arrgh and Bluster, so as soon as he had an opportunity, he also took his share. As his shipmates had done before him, he divided the cookies into three groups, and there was one cookie remaining, which he gave to Squawwk. Cruft took one group of cookies and arranged the other two groups on the plate.

Later, after their traditional hearty lunch of gruel and pickled fish noses, the pirates turned to the plate of cookies. Although each of them noticed that there seemed to be fewer cookies than they remembered, no one said anything because they were all embarrassed. Instead, they divided the cookies into three equal shares, and gave the extra cookie to Squawwk.

How many cookies did the pirates bake? (There is more than one possible answer.)