
Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?

Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?
Andrea’s only timepiece is a clock that’s fixed to the wall. One day she forgets to wind it and it stops.
She travels across town to have dinner with a friend whose own clock is always correct. When she returns home, she makes a simple calculation and sets her own clock accurately.
How does she manage this without knowing the travel time between her house and her friend’s?
You’re given a choice between two gifts: $5 and $1,000. You can choose either, but a bystander will give you $1 million if you choose irrationally. Can you do it?
See also Kavka’s Toxin Puzzle.
What do these words have in common?

A Christmas puzzle by J.C.J. Wainwright, from the American Chess Bulletin, December 1917.
White to mate in one move.
A woman visits a jewelry store and buys a ring for $100.
The next day she returns and asks to exchange it for another. She picks out one worth $200, thanks the jeweler and turns to go.
“Wait, miss,” he says. “That’s a $200 ring.”
“Yes,” she says. “I paid you $100 yesterday, and I’ve just given you a ring worth $100.”
And she trips lightly out of the store.
What do these words have in common?