Although the solution is engraved into the brain of anyone who ever played 'Hitch-Hiker's Guide', the problem itself bears repeating, as it was deliberately and cleverly designed to mock and frustrate the player's efforts. Indeed, the rest of the game ran along those lines, but the Babel Fish puzzle is the most notorious on account of the fact that it appears quite early on in the storyline. It breaks one of the cardinal rules of constructing text adventure puzzles, in that the solution is impossible to rationalise in advance, but it does so with such charm and devilish ingenuity that it is forgivable.
Essentially, after awakening in the hold of a Vogon constructor ship, the player - as Arthur Dent - must retrieve a Babel Fish from a Babel Fish vending machine. In the book and television series Dent's friend Ford Prefect simply pressed a button and collected the fish from a pan, after which the book explained to the audience the significance of the fish and its role in causing "more and bloodier wars than anything else in the history of creation".
In the game, life is not so simple. After the player presses the button, the fish is vended, but with such force that it flies across the room and into a hole. The sequence of events for the novice player goes as follows:
Above the hole is a hook, from which the player eventually decides to hang his dressing gown; this causes the vended Babel Fish to hit the gown and drop to the floor...
... where it falls down a drain ('press button and catch fish' is not a valid input). The player may then decide to block the drain with his handy towel, which causes the fish to hit the gown, drop to the floor, and land on the towel...
... where it is cleaned away by a cleaning robot that dashes into the room, and dashes out again via a small panel. At this point the player realises that the game is toying with him or her. Undefeated, he or she may choose to block the panel with Ford Prefect's satchel*, at which point the Babel Fish flies into the gown, drops to the floor, the robot picks it up, runs into the satchel, and throws the fish in the air...
... where it is cleaned away by another cleaning robot, one tasked with maintaining the upper half of the room. It is this additional puzzle that caused players the most anguish, as the solution is not at all obvious - it involves placing some junk mail on Ford Prefect's satchel, which, when sent flying through the air, occupies the second cleaning robot enough for the Babel Fish to arc gracefully into the player's ear.