The 64,000 Dollar Question was a popular United States television game show.
It is a descendant of a radio game show going back to the 1940s (date?), originally called The 64 Dollar Question. The host asked contestants a series of questions, each more difficult than the preceding one, for ever greater amounts of money, up to the last one, worth 64 United States dollars if the contestant answered correctly.
The phrase "The 64 Dollar Question" became slang for a particularly difficult question or problem.
Strangely the phrase 'the 64,000 dollar question' is common in Britain, where it means 'the most important question', despite the fact that the original game show is virtually unknown in the UK. Later, there was a British adaptation of the show (still called The 64,000 Dollar Question).