On-Air Challenge: The four rarest letters in the alphabet are J, Q, X and Z. You are given a familiar word and must change one letter in it to a J, Q, X or Z to get another familiar word. For example, given the clue "enact," the answer would be "exact."
Last Week's Challenge: This Hat Rack Puzzle by Sam Loyd was published 100 years ago in Woman's Home Companion: A hat room contains a wall with 49 pegs, arranged in a 7-by-7 square. The hat clerk has 20 hats that are to be hung on 20 different pegs. How many lines, containing four hats in a straight line, is it possible to produce? A line can go in any direction: horizontally, vertically or obliquely. To explain your answer, number the pegs in order, from 1 in the upper left corner to 49 in the lower right corner; list which pegs you put the 20 hats on, and give the total number of lines containing four hats in a row.
Answer: 18 lines. Listener Blaine Deal's weekly blog about the Weekend Edition Puzzle challenge explains the seven ways in which the hats can be arranged to get 18 lines.
Winner: Jed Martinez, Margate, Fla.
Next Week's Challenge: From listener Adam Cohen, of Brooklyn, N.Y.: Think of a former world leader whose first and last names both sound like things you might see in a mine. Who is the leader, and what are the things?
If you know the answer to next week's challenge, submit it here. Listeners who submit correct answers win a chance to play the on-air puzzle. Important: Include a phone number where we can reach you Thursday at 3 p.m. Eastern.