NPR Sunday Puzzle (Mar 24, 2013): Five by Five Word Square

NPR Sunday Puzzle (Mar 24, 2013): Five by Five Word Square:

Q: Take the four words "salt," "afar," "lava" and "trap." Write them one under the other, and the words will read the same vertically as horizontally. This is a word square of four-letter words. Note that the only vowel in this example square is an A. The object of the challenge is to create a five-letter word square using only common, uncapitalized English words, in which the only vowel in the entire square is A. The word in the center row, and column, is NASAL.

Aside from subjecting you to some obvious clues, there isn't much I can add, so I'll just give you a picture of the grid & let you figure it out from there.

Edit: "Aside from" = APART, "Subjecting" = things you might study as in PANDA (zoology), DRAMA and ATLAS (geography). The last clue was "& let" since the consonants in "aMPeRSaND LeT" are the ones used in the puzzle.

A: PANDA, APART, NASAL, DRAMA, ATLAS

NPR Sunday Puzzle (Mar 17, 2013): Water, Water, Everywhere

NPR Sunday Puzzle (Mar 17, 2013): Water, Water, Everywhere:

Q: Take an eight-letter word for something used in water. Phonetically remove a word for something else used in water. Squish what is left together. The result, phonetically, will be a verb describing what water does. What words are these?

Edit: In my comment, I said "See, I'll..." as a hint to the chemical symbol of Cl

A: CHLORINE = CL(OAR)EAN --> OAR and CLEAN

NPR Sunday Puzzle (Mar 10, 2013): As the Saying Goes

NPR Sunday Puzzle (Mar 10, 2013): As the Saying Goes:

Q: Think of two familiar three-word sayings in which all three words are the same length. The middle word in both sayings is the same. In each saying, the first and last words rhyme with each other. What two sayings are these?

Maybe these sequences will provide a clue: 0, 0, 8, 102... and 1, 9, 41, 129...

Edit: The sequences above are found in the Online Encyclopedia of Integer Sequences (OEIS) as A001575 and A001846. The phrases were first recorded in the years 1575 and 1846, respectively.

A: "Haste makes waste" and "Might makes right".

NPR Sunday Puzzle (Mar 3, 2013): Dinner Party Musical Chairs

NPR Sunday Puzzle (Mar 3, 2013): Dinner Party Musical Chairs:

Q: Eight people are seated at a circular table. Each person gets up and sits down again — either in the same chair or in the chair immediately to the left or right of the one they were in. How many different ways can the eight people be reseated?

For this puzzle, I think we have to assume each seat position and person is unique. Also, I assume Will wants seating arrangements where each person has their own chair (no sharing). What I don't see, is why the table has to be circular. Couldn't it be square and we could still figure out how to move left or right?

Edit: The first case that might get overlooked is everyone returning to their original seat. The next two cases are where all 8 people move clockwise or counter-clockwise one seat. There can't be any other cycles involving more than two people because that would require someone to move more than one seat, so the remaining cases involve neighboring "couples" swapping seats while others stay still. All that is required is to enumerate the ways to swap couples.

A: There are 49 ways that 8 people could stand up and be reseated (link to PDF containing diagrams). Incidentally, the Online Encyclopedia of Integer Sequences has the answers for various table sizes (A0048162 = 1, 2, 6, 9, 13, 20, 31, 49...) which confirms the answer for 8 people is 49 ways.