Puzzle: Nesting Words
Here's a simple puzzle that might be trickier than meets the eye.
Consider the four-letter word MEAT. If you remove the first letter, you get the three-letter word EAT, which is nesting withing the word MEAT. Likewise, if you remove the second letter, you get the three-letter word MAT. And if you remove the third letter, you get the nesting word MET. However, if you remove the fourth letter, you get MEA, which isn't a common three-letter English word.
Here's the puzzle: can you identify a four-letter word where all four or its nesting three-letter words are also valid words? All of the words must be common English words. They cannot be proper nouns (such as Lou), abbreviations (such as E.S.T.), or partial words like prefixes or suffixes (like NEO-). If a common dictionary (like the Oxford English Dictionary or the Merriam-Webster dictionary) says it's a stand-alone word in English, that's sufficient.
It's trickier than you might think. As an extra challenge, see if you can do it using only raw brain-power (as opposed to, say, some sort of computer program).
To prove it's possible, here's a solution that I was able to find. >!BOAT!< has four nesting words: >!BOA, BAT, BOT, and OAT!<. Another possible solution is >!FOUR!<, with the nesting words >!OUR, FUR, FOR, and FOU (an obscure word in the Oxford English Dictionary meaning "drunk" or "intoxicated")!<. Can you find any others? Happy solving!