Question: Queens can move horizontally, vertically and diagonally any number of spaces as illustrated. One piece 'attacks' another if it moves to the same tile that the other piece is on. How can you arrange eight queens on the board so they cannot attack each other?
Hint: Four must go on black and four on white.
Answer: Here are the two solutions. This is usually solved with guess and check although using logic may be faster. We know that each queen must be in it's own row vertically and horizontally. We also know that 4 of the queens must be on white and 4 on black. This is true because with 4 queens on the same color all of the rest of that color is venerable to attack. (It could be done with math).
Question: Your friend tells you about a story he once tried to impress a young lady with, but instead got a slap in the face. He wants you to attempt to see the flaw: It was a hot and windless day, in our bunker, when suddenly one of ours yelled: "Enemy!" We opened fire on them, leaving one hundred of them dead before they retreated. I was checking a dead captain's glasses when the shout came that they were incoming again, and the CO ordered us to open up on them with our mortars, when I yelled: "Cease fire! They're Americans!" Later, an American colonel thanked me for my work after I said that I saw their flag, waving back and forth in the wind. What is wrong with this story?
Answer: At the beginning, it was said that "It was a hot and windless day," yet at the end, it is said that "The flag was waving back and forth". Had it been windless, the flag would have been limp.