A Word Game In Rare Form

Jun 18, 2011
Originally published on June 22, 2011 2:50 pm

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.

Note: On this week's edition of the "Weekend Edition Sunday Puzzle," Will Shortz misspelled the word "siege." Plus, some listeners heard Will Shortz and guest host Jacki Lyden talk about making jewelry out of xenon. Xenon, however, is a colorless gas. We regret the errors.

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?

Submit Your Answer

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.

Copyright 2017 NPR. To see more, visit http://www.npr.org/.


And joining us is puzzle master Will Shortz. Hi there, Will.


LYDEN: Would you repeat the challenge from last week? I have to say I particularly like this one because it's called The Hat Rack.

SHORTZ: You like hats?

LYDEN: I do.

SHORTZ: It came from the great Sam Lloyd, and this puzzle actually appeared exactly a hundred years ago in the Women's Home Companion. I said a hat room contains a wall with 49 pegs arranged in a seven-by-seven array. The hat clerk has 20 hats, which are to be hung on 20 different pegs. How many lines containing exactly four hats in a straight line is it possible to produce.

LYDEN: Yeah, a lot. A lot would be my answer. And the answer, Will?

SHORTZ: The answer is 18 lines. One of our listeners, Blaine Deal, has got nice diagrams of the solution. And you go to his website, Puzzles.Blainesville.com, that's B-L-A-I-E-S-V-I-L-L-E-dot-com, and you'll see them shown.

LYDEN: This puzzle was even tougher than the challenge the week before because fewer than 200 listeners submitted entries this week. From those who sent in correct answers, our randomly chosen winner is Jed Martinez of Margate, Florida. Hello, Jed.

JED MARTINEZ: Hello, Jacki.

LYDEN: Wow, this was really a tough one. How did you work it out?

MARTINEZ: Well, basically the old-fashioned way. I was in a restaurant with some friends and we simply broke out our pens and took some napkins and just started drawing the illustration of the seven-by-seven configuration of the pegs and I just happened to come up with the answer.

LYDEN: Were you eating at the same time?

MARTINEZ: Well, we were waiting for our food to arrive while we were doing the puzzle at least.

LYDEN: Well, are you ready to play with Will Shortz now?

MARTINEZ: Well, I've waited 20 years for this moment. I am as ready as I'll ever be. Let's go for it.

LYDEN: Will, meet Jed. Let's play.

SHORTZ: All right, Jed and Jacki. The four rarest letters of the alphabet are J, Q, X and Z. I'm going to give you some words. For each one, change one letter in it for a J, Q, X or Z to get another familiar word. For example, if I said: enact E-N-A-C-T, you would say exact, changing the N to an X. Number one is gauge G-A-U-G-E.

MARTINEZ: OK. That would be gauze with a Z.

SHORTZ: Gauze, making a Z. Excellent. Number two is insure I-N-S-U-R-E.

MARTINEZ: Injure with a J.

SHORTZ: Injure, good. Guest G-U-E-S-T.


SHORTZ: Excellent. Contest C-O-N-T-E-S-T.

MARTINEZ: Context.

SHORTZ: Excellent. Panamas P-A-N-A-M-A-S.

MARTINEZ: Pajamas.

SHORTZ: Good. Coating C-O-A-T-I-N-G.

MARTINEZ: Coaxing.

SHORTZ: Excellent. Tweeter T-W-E-E-T-E-R.

MARTINEZ: Oh, tweezer.

SHORTZ: Nice. Suaver S-U-A-V-E-R.

MARTINEZ: Oh, quaver.


LYDEN: Good heavens.

SHORTZ: Election E-L-E-C-T-I-O-N.

MARTINEZ: Would that be ejection?

SHORTZ: Yes, it would. Convey C-O-N-V-E-Y.


SHORTZ: Um-hum. Seige S-E-I-G-E.

LYDEN: Carpe diem.


SHORTZ: Seize, yes. Seize the moment - good clue, Jacki. Empress E-M-P-R-E-S-S.

MARTINEZ: Express.

SHORTZ: Um-hum. Protector P-R-O-T-E-C-T-O-R.

MARTINEZ: That would be projector.

SHORTZ: Um-hum. Suite S-U-I-T-E.

MARTINEZ: Oh, quite.

SHORTZ: Quite, excellent.

LYDEN: Oh, excellent.

SHORTZ: Quarto Q-U-A-R-T-O.

MARTINEZ: OK. Maybe I'll need your help on this one, Jacki.

LYDEN: A mineral.

MARTINEZ: Oh, quartz.

SHORTZ: Quartz is it, good. Function F-U-N-C-T-I-O-N.

MARTINEZ: Oh, junction.

SHORTZ: Junction is it. Tenon T-E-N-O-N. Those short words, short words...

MARTINEZ: Oh, a xenon.

SHORTZ: Xenon, nice job. And here's your last one: stargate S-T-A-R-G-A-T-E.

MARTINEZ: Oh boy. Stargate, stargaze.

SHORTZ: Stargaze. Nice job, Jed.

MARTINEZ: Thank you very much, Will.

LYDEN: And for playing our puzzle today, you get a WEEKEND EDITION lapel pin and some puzzle books and games that you can read about on our website, NPR.org/Puzzle. And before we let you go, tell us what member station you listen to.

MARTINEZ: I am equally located between two NPR stations. To the north in Palm Beach County, there's WPBI; and to the south in Miami-Dade County, WLRN.

LYDEN: Well, Jed Martinez in Margate, Florida, thanks for playing the puzzle with us and getting all those words from xenon to stargaze.

MARTINEZ: Thank you. And thank you, Will.

LYDEN: What's the challenge for next week?

SHORTZ: Yes, it comes from listener Adam Cohen, of Brooklyn. Think of a former world leader whose first and last names both sound like things you might see in a mine. Who is it? So again, a famous 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?

LYDEN: Well, this was really fun, Will - as usual. Thanks so much.

SHORTZ: Thanks a lot, Jacki. Transcript provided by NPR, Copyright NPR.