## Sunday, November 02, 2014

### NPR Sunday Puzzle (Nov 2, 2014): An Apt Time for a Clock Puzzle

NPR Sunday Puzzle (Nov 2, 2014): An Apt Time for a Clock Puzzle:
Q: Write down the following four times: 3:00, 6:00, 12:55 and 4:07. These are the only times on a clock that share a certain property (without repeating oneself). What property is this?
I guess we all have an extra hour to figure this one out this week...

Edit: Time's up!
A: The intended answer is that the four times given visually form Roman numerals L(50), I(1), V(5) and C(100). (The other Roman numerals (M, D, X) can't be easily formed so are excluded.)

I take issue with the misleading wording (only times?) and that we have to visually view two straight hands as forming a curved letter of 'C'. I'm sure there will be some that call this puzzle bogus and you would be justified in saying so, but remember I'm just the messenger.

1. Here's my standard reminder... don't post the answer or any hints that could lead directly to the answer (e.g. via a chain of thought, or an internet search) before the deadline of Thursday at 3pm ET. If you know the answer, click the link and submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't give the answer away. You can openly discuss your hints and the answer after the Thursday deadline. Thank you.

2. Turn, turn, turn, turn.

1. Does this mean you've solved the puzzle?

2. I have an answer, yes.

3. Confirming my worst fears.

4. You've been quiet this week, WW.
After benmar's clarification, I stopped turning clocks in my sleep.
Is it worth revisiting?
Worst fears, indeed! Not that election night is helping, either.

5. I sense a scenario developing here...

Rachel: Last week's on-air contestant was jan, who comported himself very well in the on-air challenge...
Will: Yes, Rachel, and this week's on-air contestant should also do well. She is the ONLY listener this week to submit a correct solution to our puzzle. She is Word Woman, and like jan last week, hails from Blainesville.
Rachel: Wow, Word Woman. How did you solve this week's tough puzzle?
WW: Well, Rachel and Will, I just...

(to be continued)

LegoCliffHanger

6. Wheel see. . .

7. WW, I should have written you in as a candidate on Tuesday. Congress needs brains like yours!

8. "Turn, turn, turn, turn" referred to getting a few more turns or curves to make 4:07 into a true C. I saw the L, I, V Roman Numerals right away with Blaine's illustration. The C needed some work.

"Wheel do" referred to a Roman water wheel.

Yes, I got SuperZee's 156 clue.

Yeah, not Will's finest effort. . .

3. Jan -

Great job on one of the hardest puzzles I can remember!

1. Nice job on the air, Jan. And a shout out to the blog too! You make me proud.

4. Jan -

Yep - Yours was an excellent showing on a very difficult puzzle (IMHO).

Chuck

5. Just curious if anyone has solved this week's puzzle. I'm finding myself going in circles on this one and am sure I'm missing something. Analog, digital, hours, angles, upside-down, words, letters, semaphore, etc. Am I making it too complicated?

1. Requires some turning & simple math. Hope you don't delete this.

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6. The first thing I did was turn it upside down. No luck yet.

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7. Each can be spelled out using only the Hungarian equivalents of the letters in MAGDA GABOR. No other toothpaste can make this statement.

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8. I have absolutely no idea what the answer to the challenge is, but I am really impressed with Blaine's illustration of it! Is this a stock photo that we would find next to the answer if we Googled correctly? Or have you created it with your bare hands from raw pixels?

And congratulations to jan on a fine performance!

1. It's not a stock photo, but I did use an applet to generate the images of each clock.
Analog and Digital Clocks

2. There are myriad reasons to visit and post on Blainesville. One of them is the "look" of the blog. Every week, Blaine gives us a top-notch, creative, interesting illustration of Will's weekly puzzle. He is a master of design (note his banner-logo.)

Blaine is also the ultimate benevolent blog administrator. He is there when we need him, tactfully inconspicuous when we don't.

This is just a fantastic forum for our forays into puzzledom, opinion, punnery and funnery. Thanks, Blaine.

LegoNotJustFunnin'

9. Blaine, I spent about half an hour going through the same kinds of things that you did. I even called up an animated clock (http://www.visnos.com/demos/clock) to play with the hands and look at angles etc. with simultaneous digital display. I got nothing. You are not alone.

10. Oh, and in desperation I even Googled the list of times. It just returned a bunch of garbage, like long lists of marathoners' times.

1. Hi Rakewell,

I did the same thing, but I have to disagree with you. Some of the Google results I found to be very interesting, such as a railroad newsletter from the early 1900's that contained all sorts of advertisements aimed at the railroad ridership as well as offerings of railroad equipment aimed at the railroads themselves.

Thanks -- Phil J.

P.S. Haven’t solved it yet…

11. I too have tried all these things plus Roman Numerals, but am getting nowhere fast. I was going to drive to Gasworks Park, where there is a magnificent sundial, but this is Seattle, so what would be the point?

12. Wow! I tried all those things, too, (well, not Googling) before checking in here. This must be a toughie if it is stumping participants here. It will be fun when someone posts that an answer has been found, but the someone is not going to be me.

13. One correct answer: All four of those times--and ONLY those times--were mentioned in a puzzle by Will Shortz on November 2, 2014.

What do I win?

14. Does it give any clues to anyone here that Will had to include the strange parenthesis "(without repeating oneself)"? What does this mean? Surely he doesn't think that we'd believe that an answer would be 3:00, 6:00, 12:55, 4:07, and 4:07.

1. I've scratched my head over that, too. It may mean nothing more than 12:55 a.m. is the same "property" as 12:55 p.m.

Or it could hold the master clue to solving the whole thing. I sure don't know.

2. Ugh. I'll say that I think it is an inelegant clarification which means the times are a minimal set to exemplify the property...but additional times may fulfill the property, albeit redundantly. If that's the case, I would have suggested better wording might be, "These four times are the only ones needed to show a unique property." I wonder/hope if this interpretation is similar to others', leading to a plausible but still somewhat dissatisfying (considering the wording of the question) answer?

15. Jan,
C U @ 3, non, 6, non, 12:55, non 4:07.

16. I can't believe that no one else has stumbled on the answer.

1. I'm turning and tilting, clockwise and counterclockwise, but nothing is making sense.

2. Consider upon a turn or a twist coming up with a different time & a little math which equals xyz x 4!!!

Don;t know what else I can say before Thursday.

3. 2 properties that are definitely NOT the answer:

I just wanted to be sure benmar12001 really has discovered a property that those 4 times share, but which is NOT shared by ANY OTHER time.

I had an idea that come Thursday, noon PST, we saw a post of something like "I calculated the exact number of degrees that the hour hand had moved, and that the minute hand had moved since midnight (or noon) in the case of all four of those times, and in ALL FOUR of those times the minute hand had moved EXACTLY 12 TIMES as much as the hour hand!!!

The minute hand is ALWAYS moving 12 times as fast as the hour hand, so that "property" is shared by any time you'd like!!

Also, 3:00 is NOT the only time in which the hour hand is exactly 90° clockwise from the minute hand, neither is 6:00 the only time in which the hour hand and minute hands are 180° apart. Neither of those four times have a unique claim to the number of degrees of angle separating the hands. Take ANY time you'd like, and measure the number of degrees between minute and hour hand. That EXACT same angle of separation will be between the same two hands in exactly 1 hour, 5 minutes, and 27 3/11's seconds. (That's exactly 1/11th of 12 hours.)

4. My problem is if I turn a time (say 6 o'clock), there is no valid time that has the hour hand exactly on a number, so no rotated time makes sense. For example, if we tilt it 90°, it kind of looks like 9:15, except then the hour hand should now be closer to the 10, not directly on the 9. I must be on the wrong track.

5. I got it. Blaine's picture was a big help

6. Blaine,

After 6:00, the hands are again 180° apart at 7:05:27 3/11, then again at 8:10:54 6/11, then again at 9:16:48 9/11, then again at 10:22:16 1/11, then again at 11:27:43 4/11, then again at 12:33:10 7/11, then again at 1:38:37 10/11, then again at 2:44:05 2/11, then again at 3:49:32 5/11, and then again at 4:54:59 8/11, before 12 hours later, at 6:00 again.

7. EaWAF, I completely understand that any configuration of the hands happens 11 times in 12 hours. But that exactly makes my point that a rotation by 30 degree increments doesn't result in a valid clock configuration so I don't follow benmar's hint about reading the tilted clock as a different time, at least not one with a whole number of minutes...

8. I believe that you need to tilt so many degrees each time using your clocks above & do some math that demonstrates a unique mathematical similarity.

9. Enya & Weird Al:
You have shown me the way. I believe my answer is wrong. Apparently a 90 degree tilt resulting in 3:00 - 6:15; 6:00 - 9:15, 12:55 - 4:10, and 4:07 -7:22 resulting in a 3hour and 15 minute difference applies to any clock time, not just these 4.

10. Gee, does this mean that (like me) everyone has drawn a blank on this week's puzzle so far?

17. This puzzle has been making my head hurt. I super glued my clock radio to my bedside table in order to impede my tendency to throw the damned thing across the room when it goes off and I am not awake. This caused me to need to stand on my head in order to read the digital numbers upside down. Now my head hurts.

18. I can see where the hour and minute hands in three of the configurations are pointing directly to whole numbers, but the last one does not do this.

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20. Let's all try to remain civil this week.

1. I'd like to, but can't help continuing to wonder why 4:07 is particularly more appropriate than 4:06 or 4:08 (e.g.).

2. ... or why 12:55 is better than 1:50, etc. That can't be the gimmick.

3. Don't Be mean.

4. mike_ and jan,

The following is in response to your consecutive comments from Monday morning (8 AM and 9:23 AM):

I am not sure, mike, but I think the reason 4:07 is better than 4:06 is that there is already a “6” being used (in the 6:00), thereby somehow satisfying the parenthetical clause “(without repeating oneself)”.

Note that the clock times comprise the following list of “raw” integers: 0 0 0 0 0 1 2 3 4 5 5 6 7. (We can probably ignore the zeroes.) Maybe 4:07 is better than 4:08 because you have to “use up” a 7 before you can use an 8?

Or, jan, “why 12:55 is better than 1:50, etc.?” Maybe because repeating digits is taboo (notwithstanding the double-nickels in 12:55!!!) Maybe 12:55 is okay because it is considered as a fifty-five instead of a five and another five?

I have discussed my thoughts about this puzzle a bit more in depth on Puzzleria! I don’t want to put our esteemed blog administrator on the spot if I somehow unwittingly spill some magic puzzle-solution beans. No, I don’t think I have solved this puzzle but, if “4:07” was something like 1:10 or 2:05, I would feel as if I was pretty close to solving it.

This is exactly what a good puzzle should do… make us crazy! Even if we groan and cry “Foul!” when we finally hear Will’s (or Al’s or Berf’s [see below] answer, at least we’re having fun now.

I’m glad to see Al (Sunday, Nov 2, 9:16 AM PST) working on this puzzle. If he can’t solve it, it is unsolvable!

But maybe Berf (Sunday, Nov 2, 5:47 PM PST) has figured it out

I have not. These are not hints, just observations.

LegoPerhapsOnThePeriphery

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1. Thanks, Lego!

2. PlannedChaos,
The following is about as civil as I get:

jan definitely did Blainesville proud!

He pulled no punches. He mentioned, for instance, that Eva Gabor popped up (not out) in a recent NPR puzzle. He then asked Will the great question about the NYC crossword content occasionally foreshadowing the NPR puzzle content. (Will gave the “non-answer answer” that we have come to expect of folks for whom we should not be voting tomorrow. It’s okay, Will, there’s nothing wrong with a little cross-pollination of your crossword and NPR puzzle gigs. We understand.)

And then, to top it all off, jan gave a nice shout-out to Blaine (and us Blainesvillians!). Amazingly, none of this was edited. NPR must have trusted him as an honest and sincere on-air contestant.

Just prior to that shout-out, jan proceeded to simply cruise through the toughest anagram on-air challenge in recent (or distant) memory. Impromptu anagrams are really tricky, and he was masterful in unraveling them. The “replace either the first or last letter” was cruel and unusual puzzlement, but jan prevailed! Bravo!

LegoVeryImpressed

22. If my solution is correct, I'd argue that 10:00 could be considered as sharing this property.

23. I looked to see if the "property" is related to the game of Monopoly, but I doubt it.

1. That really is too bad.

2. Car Talk was perhaps my favorite radio show, and I'm not even a car guy. I was just now posting about the rarity of creative genius over on Puzzleria! when I heard of Tom Magliozzi's passing.

Tom, age 77, and his brother Ray had true creative genius, IMHO, and they were entertaining as all get-out! A great loss. I know he had a lot of fans (and impersonators!) here at Blainesville.

Lego...

But, look at it this way:
Heaven may finally get that much-needed tune-up.

4. I'm not sure the blasphemy associated with owning a '66 Dart or an old MG qualifies you for that kind of afterlife..

5. Well, wherever Tom ends up...I hope -- a long time from now -- I end up there, too.
RIP!

25. Blaine:

Sunday night a friend of mine (let's call him Beatles_and_Melanie_fan) ventured a suggestion to which I thought "Doubtful. I really think it would be terrible if that turned out to be the answer; but I supposed we could keep that terrible suggestion in our bucket of ideas; but let's BOTH HOPE that we can eventually think of a much better answer before Thursday noon (our time - PST)."

Anyway, yesterday after reading benmar12001's confession, my friend asked me if I had any ideas. When I answered that all I can think of was that terrible idea of his, he said something like "Oh, PLEASE!!! That would make this A REALLY TERRIBLE PUZZLE!!"

I agree with him, but still haven't thought of ANY OTHER possible answer!

Blaine, I wonder if this one time you might give me permission to post my friend's terrible suggestion of an answer, even if only that all of us on this blog might join together in hope and prayer that it DOES NOT turn out to be what Will is expecting?

1. I'd advocate for just hinting at your possible solution -- and if you did already, I missed it -- I think there's a possible solution which isn't overly terrible, and is shared by a couple folks here. More like an interesting answer searching for a better puzzle.

So if that is the answer, I think that the clarity of the wording of the puzzle is more of the problem -- similar to the blue-eyed folly of a fortnight ago.

2. I really hope this puzzle has an elegant solution. The last puzzle by this author was the AFGHANISTAN HIJAB and apart from being something that not everyone would know, at least we can agree it isn't a bogus puzzle.

I'm all for people posting their failed "solutions" (assuming that it really can't be the answer). I don't think it will take anything away from the real answer.

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5. Yes -- it reminds me of a very big clue. Yikes!
Try applying it to some of my suggested alternative phrasing, and see what you (and your friend with different taste in music) think...

6. If that is the answer (and it would fit with PC's hint), then I really don't like it. Those 4 times create a set, but there are definitely other times that create the same set. It also stretches things to say 4:07 looks like part of the set. Agreed?

7. Def agreed. Unfortunately! But if it didn't include 4:07 (e.g.), we'd probably have a larger argument that maybe it should.
If we think of the 'without repeating oneself' clause to applying more to the property itself, it seems to make sense. Note that no other times would represent the property without repeating it.

Like I said, thinking about it that way, it's sort of an elegant answer in search of a more elegant question. But that's also often how puzzles are derived, if not written!

Consider the alternative, that there is another property shared only by these 4 times by sheer coincidence.
It took me a full day and night finally to accept this possibility and be at peace with it. Mostly. :)

26. Still banging my head against the wall on this one. Maybe someone in Chicago can pump the puzzle's author for hints.

1. From what I can tell, from prior times when his puzzle was selected, he won't give anything away until after the deadline... which I respect, even if I wish I could figure this out.

2. jan -- nice job OTA, BTW! -- based on our previous discussion, if the puzzle were more clearly stated as
"These are some of the only four times that share a certain property"

What I am thinking is, as we all know with puzzles, often times the way we describe something we already know doesn't fully account for reasonable interpretations by a naive brain...because we're already biased with the answer!

Once you have that answer, and re-apply it to the original question...one might see how it arguably fits the somewhat ambiguous phrasing.
I wonder if this helps anyone, or puts us on the same track at least?

3. I also wonder if the order of the times matters. In the order they happen in a 12 hour period, they would be 12:55, 3:00, 4:07, 6:00. So why would they be given in the order of the puzzle?

4. I tried looking at the 8 x 8 matrix including 00:55, 03:00, 04:07, 06:00, 12:55, 15:00, 16:07, and 18:00. Nothing interesting leapt out at me.

5. I've been wondering about PC's use of "civil".

6. @Blaine: although the wording of the puzzle already isn't perfect, I would argue that, if the order of the times mattered, the puzzle should say, "Consider the following sequence of times..."

@Paul: Last time the wording of the question was poor, I think observations about Will's personality and integrity were called into question!
Nonetheless, whether the answer is TERRIBLE, there is at least one excellent, subtle clue (not mine) hinting at a possible shared answer.

7. So would 6:00, 12:55, 3:00, 4:07 be a better order?

8. @mike: I've never uttered the word TERRIBLE in my life! You may be thinking of Rolling Stones_and_Sheryl Crow_fan. It happens.

27. I hope I'm not being rude, but maybe 4:09 would have been better than 4:07. Or 9 and 3/13 minutes after 4. And 55 and 5/13 minutes after 12. But 4:09 and 12:55 to the nearest minute. The 3:00 and 6:00 are fine as is, it seems to me.

One common order is 4:09, 6:00, 3:00, and 12:55.

Unrelated, I hope, what's the rule to get from one number to the next in the sequence 12:55, 4:07, 1:03, 3:00?

1. ''number" should be "time."

28. Lego’s Lament (warning: mixed metaphors ahead!):

As I fail miserably to think outside the box on this puzzle I succeed smashingly in seeing only inside the tunnel. My latest “if-only…” clock settings: 3:00, 6:00, 12:54 and, holding my nose, 8:07.

Is it possible I’m on the right track? Nein! Indeed I’ve skidded completely off the rails. For those of you still on the rails and inside the tunnel, I hope there is a light at the end of it for you. Me, I am but a mongrel that’s latched onto a delicious bone and cannot bring myself to let go.

LetgoTunnelVision=Blinders

1. Disregard the phrasing about these being the only times... instead think of these times fully defining a set of 4. While you can swap out one time with another (say 4:07 with 4:05) you must have 4 times with these specific properties.

I have mixed feelings about the puzzle, but I think it must be the intended answer.

29. What is the record for the smallest number of correct answers submitted for one of these puzzles. Based on the comments above, I'm guessing a new record will be set. Maybe as few as 156.

1. I believe there was a math puzzle many years back where there was only one correct answer.

2. I never did find it online, but I distinctly remember a strange puzzle that Will gave years ago involving shifting letters of the alphabet etc., which the following week he had to admit was botched in its construction, so there were no correct answers.

3. I remember one, within the last year or two, where there were 15 correct responses. I don't recall which puzzle it was.

4. The puzzle you are thinking of was another one involving clocks. SHE and HIS puzzle.

There was a puzzle that was something like this. Think of a word for an article of clothing. Take its ROT13-reverse, and get a word for a crime. ROT13-reverse is to replace each letter of a word with the letter that is 13 places different in the alphabet, and then reverse the order of what results. So the ROT13-reverse of ``ABC'' is ``PON'' because A goes to N, B goes to O, C goes to P, and then you reverse the result.

I think the intended answer was ``garment, larceny.'' This clearly does not work as the ROT13-reverse of garment is garzent, and the ROT13-reverse of larceny is larpeny. But, nothing else comes close.

There was only one submission, and that one said there was no solution.

6. Wow! Thanks for the info! A case of "close, but no cigar"!

7. The garment/larceny puzzle was from July 2003.

8. BTW, SuperZee, kudos for smuggling in the number 156 (the total of the four Roman numeral values). I was wondering if anyone was gonna show that number and you did!

How many others of you noticed?

9. Both Florida Guy and Blaine have either great memories or far superior internet search skills in finding the "puzzle without a solution" that I had referred to. But just for the record (and because the answer to this week's challenge is so disappointing) both the Topica website and FG say, "Garment becomes garzent; larceny becomes larpeny." Actually, with Rot-13 and reverse, garment becomes larpeny and larceny becomes garzent.

10. I hate to break it to you, but the Topica website and FG are right and you are wrong!

GARMENT rot13's into TMEZRAG, which reverses into GARZENT, and
LARCENY rot13's into YNEPRAL, which reverses into LARPENY.

And can we limit our replies on this particular reply thread to yes's or no's to the question "Did you notice the 156 in SuperZee's post to which all these replies are?" (And what is the grammatically correct way to phrase that last question?)

11. Ah, screw it! I'm trying again.

I hate to break it to you, Bob Kerfuffle, but the Topica website and FG are right and you are wrong!

GARMENT rot13's into TNEZRAG, which reverses into GARZENT, and
LARCENY rot13's into YNEPRAL, which reverses into LARPENY.

And can we limit our replies on this particular reply thread to yes's or no's to the question "Did you notice the 156 in SuperZee's post, in response to which are all these replies?" ?

30. Whiskey sherry.

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32. There was a puzzle involving making words out of symbols from the periodic table. The answer was REALER. I think there were about 5 correct entries.

33. Wasn't there only one correct answer to a fairly recent puzzle where we were invited to fill in the U.S. towns with the total highest population to form a crossword block puzzle?

34. I have an answer, but I can't say I'm happy about it.

The way my answer works, the order of the times DOES matter, and they are not in chronological order. And there is a reason for 4:07 as opposed to 4:09.

I am not using legolambda's idea of "using up" the numbers.

And (answering "why 12:55 is better than 1:50, etc") I hope I am not giving away too much if I note that 4:07 is 3 hours and 12 minutes after 12:55.

35. I like 4:09.230769231 - it's unique regardless of other clock properties.

I will be delighted if 4:07 is indeed unique, and the answer is unexpected.

36. Regarding puzzles with the least number of responses, what about puzzles with the most responses? I submitted a puzzle that resulted in over 3,000 responses. Interestingly, it was not meant to be controversial, but it did generate some repartee between the on-air contestant and a "mystery guest."

Thanks – Phil J.

37. OK, it's after noon on Thursday. Will somebody please put me out of my misery by posting the answer?

1. Because of the time change, it isn't 3 pm ET yet... still one more hour to go.

38. Has there ever been a time when no one had the correct answer?

1. Read the discussion above about the flawed puzzle with the intended answer of garment and larceny. They did accept an answer that week from a programmer that proved there was no answer to the puzzle as worded.

As for this week's puzzle, it may be flawed in the wording, I still think there will be some people that submit the intended solution.

39. Thanks, Blaine.

40. Kudos to anyone that saw past the flaws in the puzzle and figured out the answer that the hands form Roman Numerals (C, L, V, I).

41. I think the intended answer is:
The 4 times, on a regular 12-hour analog clock face, kinda look like roman numerals(L,I,V,C).
It hit me Wednesday morning after reading xfyre's comment, which I see has since been removed by a blog administrator.
There may be an angular, rotational, symmetrical answer lurking out there.

It may be more elegant (wouldn't take a lot).

Then again, it may involve looking at the clock through a sheet of cellophane.

42. Here's my solution, which I really don't like.

When viewed on an analog clock, the four times can appear as the letters L, I, V and C. Taking them as Roman numerals, and without repetition, they form the number 156---which is why I guessed there would be that number of correct solutions.

43. Ok, here's my friend's terrible answer:

My hint earlier this week which Blaine deleted was "Look at Blaine's clocks picture at the top and observe the four hand positions. Do they remind you of anything?" (Well, that's not word-for-word, but Blaine deleted it.)

Beatles_and_Melanie_fan's terrible answer: On standard analog clock faces, the hour and minute hands together resemble a Roman Numeral character.

3:00 resembles an "L", the Roman numeral for 50;
6:00 resembles an "I", the Roman numeral for 1;
12:55 resembles a "V", the Roman numeral for 5; and
4:07 resembles a "C", the Roman numeral for 100.

44. Wow. That's awful. Just awful. If that's the intended answer (and I think it probably is), it may be the worst I can remember.

45. In fact, in honor of the death of Car Talk's Tom, I'm gonna say that that puzzle was BO-O-O-O-O-O-O-O-O-O-GUS!

1. My sentiments exactly!

46. As Tom Magliozzi would have said: "BOOOOOGUS!"

How is 12:55 the only time on a clock that looks like a V? Doesn't 5:05 also look like a C?

1. The hour hand is shorter than the minute hand. NOTHING looks like a V! I could go on.

47. Darn it - I am sorry, but I saw that CLVI configuration as I was trying to figure out the puzzle, and I discounted it because (as has been the discussion here) there are other times that would have made a C, and it doesn't look like a C anyway. Someone tell me there is a better answer than this, please!

48. I did not discover the answer this week although I did consider Roman Numerals, but did not make the connection. Very poorly worded and bogus in my opinion. My above post:

"I too have tried all these things plus Roman Numerals, but am getting nowhere fast. I was going to drive to Gasworks Park, where there is a magnificent sundial, but this is Seattle, so what would be the point?"

49. I really disliked this week's puzzle. A difficult brain twister is one thing; but the "clue" was just lousy and poorly worded. All in all, this has been a frustrating week. But kudos to all of you who figured out the puzzle. Namaste.

1. Namaste? You mean ave atque vale, dontcha?

2. Are there sanskrit numerals? If not, why not?

3. I should have known!

50. My friend Beatles_and_Melanie_Fan says that IF the puzzle answer is what we all seem to think it is, it SHOULD have been written like this!

Q: Consider the following four times of the Day:

3:00, 6:00, 12:55 and 4:07

These times on a clock share a certain property.

What is it?

1. Beatles_and_Melanie_fan: Elegant wording (for a very inelegant puzzle)! I particularly disliked Will's instruction to "write down" the times, which created unnecessary misdirection.

2. So, BAMF, did you see Paul McCartney at any point in his "Out There" tour?

51. Didn't we go through this with the upside down times? In that case the answer was obscure and the puzzle was unfair, but it wasn't as bad as what we (who couldn't, with a few exceptions, work out the correct answer) had come up with. So there is still hope.
In this case even the hints led me astray: when SuperZee threw out 156 (which is 12 times 13) I tried to figure out what these times would look like if we had thirteen hours on a clock face. Very Orwellian.

1. As I pointed out in a response thread back up quite a ways, 156 is the total of the four Roman Numeral values.

2. Oh I got that--just XXIV hours too late.

52. So to ease the pain of a bad puzzle, here is a bad joke:

I went to a restaurant that serves "breakfast at any time." So I ordered French Toast during the Renaissance.

Stephen Wright

1. No. Definitely, NO.

2. Henry Willis, that about made my day. Thanks, I needed that.

53. Pointless, poorly worded and could be the equal of the upside down alarm clock for all around stupidity.

Chuck

Now let me tell you how I really feel!

54. I question that 6:00 is the only way to form a single "I" 12:00 forms a single "I" since (on all my dial clocks) the minute hand is over the hour hand and obscures it. So, 6:00 must stand for two "I"s which is unique. This leads not to roman numerals, but to letters which note the change in "CIVIL" time.

As for 4:07 seems to be an attempt to put the tips of the "C" on a vertical line. but this is not unique to all clocks unless there is a standard ratio for hand lengths - so not necessarily a unique time. 4:09 was suggested to make the bisector of the angle between the hands of the "C" a horizontal line, and this is a unique time.

55. Let's also remember that Planned Chaos's admonition that we all be CIVIL to each other was right on the mark.

56. I saw the Roman numerals, but dismissed it for all the reasons stated above. I played around with all these times all week in search of an elegant answer. One curiosity I got stuck on is if you add up all the times, 300, 600, 1255 and 407 you get the sum of 2562. If you rotate the times 90 degree to the right, of in effect add 3 hours and 15 minutes to the times, 615, 915, 410 and 722, you also get a sum of 2562. I could not figure out mathematically why that would be. It does not come out if you rotate it 90 degrees to the left or 180 degrees. Nor could I find what " property" to assign to it. I looked to this blog to see if anyone else discovered that or might explain why that would be. anyone?

1. Actually, you get 2662 for the second set of times. For three of the times, you add 15 minutes and it goes to a bigger number of minutes (00->15, 00->15, 07-->25). One of the times goes into the next hour, so it is equivalent to going back 45 minutes (55->10). So those transformations cancel out the minute difference.

For the hours, it is almost the same thing. Three of the times go up by 3 hours each (3->6, 6->9, 4->7) for a total of 9 hours added. But with 12:55 it goes to 4:07 (12->4). That looks similar to going back 8 hours. That's why it is 1 hour different in their sums (2562 vs 2662).

57. I really thought the answer was to reverse the minute and hour hands, add the original time, and the hands line up. Kudos to anyone who saw roman numerals ( I saw LIV and not a letter ).

58. After removing the redundant numbers I was left with t3, 6, 12 and 47.
These are the atomic numbers for lithium, carbon, magnesium and silver.
Li, C, Mg, and Ag leaves me with the phrase, "Lic(k)'m gag."
That sums up how the puzzle whipped me and my response.

59. At first I was going with Berf and then I saw the LIV but the last one threw me off completely so I thought it was a message to go and live my life and so I became busy elsewhere LIVing La VIe en rose

60. jutchnbev -
"615, 915, 410 and 722, you also get a sum of 2562"
Sorry, that's 2662.

Blaine, are you saying you have it from the author that the Roman numeral thing is the right answer? If not, I find that hard to swallow, based on the clue - I mean, even harder to swallow than you say it is.

Thanks.

1. I haven't heard definitively so we could all be wrong, but I think it has to be. Now that the deadline is passed maybe he'll respond to comments? Puzzle #105 - Four Times

61. To keep the proper scale 12:00 better represents 'I' than 6:00.

Ole Zeke entered Ti30, Ti60, Ti125, and Ti407.
These products are the times minus just the repeated numerals.

1. I calculate that's not the right answer, but I like it better.

62. I think Lego was the most clever by his attempt at making the numbers equal their corresponding letters of the alphabet to spell out FALL BACK, which refers to our returning to Standard Time. He almost made it work.

63. I'm a newbie to this blog. Some earlier posts asked about the least and the most number of responses to the puzzle which reminded me of this: On Thursday, November 11, 2010, I had major surgery. I was home and confined to my bed on November 12 and mainly read and listened to NPR. On Saturday (11/13) I was listening to Wait, Wait, Don't Tell Me and a caller from Wisconsin won on the limerick portion of the show. On Sunday (11/14) the contestant on the Sunday puzzle was the same person from Wisconsin AND he was a first time entry. This means he got two phone calls on that fateful Thursday. What are the chances?

1. Hey, Liz, I remember that double call also. And I bet I'm not the only one. . .

2. Liz,
Hello and welcome.
This will most likely sound completely crazy to you, and most others, but while the mathematical chances are rather small, I have learned through a very few life experiences that there are no accidents. What I am saying is that I doubt it had anything to do with chance in your case. I told you, you would think it crazy, but you did ask.

3. I wrote to both shows, and both responded that yes, it was the same person. I did keep one of the emails.

4. Planning any sort of observance on the Saturday before Thanksgiving, sdb?

Curiously,
Jack

5. Paul:
I don't understand your post. What would I be observing?

6. isupp oseyo ureri ghtin allpr obabi lityt heres nothi ngtoo bserv eihad thoug htabo utdro pping somea cidan dtryi ngtof indso megra ssykn ollwh ereic oulds itand readt hechr onicl esofn arnia butim aybeg ettin gtooo ldfor thats ortof thing

64. Yesterday, after figuring out the Roman numeral connection, I wrote, "I have mixed feelings about the puzzle, but I think it must be the intended answer." I was trying to hint at the Roman numerals (M,X,D) that weren't included.

65. Ben posted on Wed Nov 05, at 10:15:00 PM PST:

I have an answer, but I can't say I'm happy about it.

The way my answer works, the order of the times DOES matter, and they are not in chronological order. And there is a reason for 4:07 as opposed to 4:09.

I am not using legolambda's idea of "using up" the numbers.

And (answering "why 12:55 is better than 1:50, etc") I hope I am not giving away too much if I note that 4:07 is 3 hours and 12 minutes after 12:55.

Ok. Ben, if you're reading this, we are now much more than sufficiently past the due date and time, so it's OK to reveal your answer.

66. I thought they might be scores from some past world series: 3 to 0, 6 to 0, 5 to 1, and 4 to 7. However, I could not find any world series with those scores....

67. There MUST be an answer to this “four-clocks puzzle” that we have not considered/discovered!

I Will give Dr. Shortz the benefit of the doubt on this one. He has had a pretty good year (2014) so far of giving us some really creative and great puzzles. If the “CLVI Roman numeral” answer that we collectively seem to assume is Will’s intended answer is indeed his intended answer… well, then Will just had an uncharacteristic off-week, IMHO. But we really don’t know the intended answer yet. We are still only speculating.

That said, I am worried that we might be speculating correctly. Why? Because there are lots of really great puzzle solvers here at Blainesville, and no one has posted a more plausible or elegant answer... yet.

For example, we haven’t heard from Al since his Sunday, November 2, 9:16:00 AM PST comment: “The first thing I did was turn it upside down. No luck yet,” to which I subsequently replied: “I’m glad to see Al (is) working on this puzzle. If he can’t solve it, it is unsolvable!”

Here is why I wrote that (See the paragraph immediately above the illustration reading “Caution, This Sign Has Sharp Edges”). If Al hasn’t deciphered a more clever solution that the "Roman Numeral answer" that we are assuming is Will's intended, then I don’t think that a more clever one exists, and this is a puzzle that is not up to Will Shortz’s high standards.

After I realized that the two-hands on the four clock faces formed an L, I, V and C, I had considered giving the hint “154, 156” (154 = CLIV, and 156 = CLVI, which is also the sum of C + L + V + I. But I did not bother to do so. Why? Well, for one reason, because the Roman numerals M, D and X were not represented. But mainly, because “these are (NOT!) the only times on a clock that share a certain property (without repeating oneself).”

Sure, 12:55 looks like a V but so do 10:10, 1:50, 11:06 etc., etc, etc… And don’t even get me started on “C = 4:07” (oops, I mean “< = 4:07”)!

I will reflect more on this week’s NPR puzzle on Friday’s (tomorrow’s) fresh Puzzleria! blog, and I will present a porcidorsaline puzzle that “piggybacks” off of Will’s offering of this week. It will be a fair puzzle, one with very careful wording. I promise. And I truly hope that Will Shortz surprises us Sunday morning with an ingeniously elegant solution. But C, L, V, I sure ain’t it!

LegoNotRushingToJudgment

68. This comment has been removed by the author.

69. My Answer was L I V & <. I saw 4:07 as < the less than sign. IV, /, \.

70. You could say IV<L (4<50).

71. Now that we're done with that puzzle, what else is new with NPR?

1. (I was particularly primed for that after hearing Hank Azaria on Marketplace yesterday.)

2. "This American Life" isn't an NPR show.

3. Yeah, and neither is Marketplace. Splitters!

4. (I hate the Romans. And their numerals!)

5. jan, I echo your remark. I have always thought of them as roamin' numerals, wandering on and on.

Be a letter or be a number but don't be both.

6. jan and Word Woman,
1 50 AGREE!
…0937 (flip upside-down… wait, I fear I’m experiencing deja-inversion-vu!)

72. When is 3>132?

1. When the big hand is on the twelve?

73. Three is greater than one hundred thirty-two when you turn old ZEKE upside down.

1. Zeke,

Even when I turned old Lego upside-down and rewrote you inequality as 3 > 13M2, I was stymied. Even in Germany, ZWEI is not less than 2.718...

LegoStymied

2. I am humbled.
Zeke the meke (sic)

74. The swag from Weekend Edition has been arriving piecemeal, including some unadvertised items, like Grammar Girl's "101 Words Every High School Graduate Needs to Know", and her "101 Misused Words You'll Never Confuse Again." Word Woman, is Grammar Girl your inevitable teenage sidekick? Do you guys have matching capes and tights? Could you use your superpowers to do something about those annoying diareses in The New Yorker?

1. Grammar Girl and I have never met or even corresponded, jan. Are the books scintillatingly useful? Let me see what I can do about the diareses of the printed word, though. Alas, no capes only capers. . .

75. Next week's challenge from Steve Baggish, of Arlington, Mass.: Name a well-known clothing company. Move each of its letters three spaces earlier in the alphabet and rearrange the result. You'll name something you don't want in an article of clothing. What is it?

1. There's a historical coincidence involving today's answer.

2. It's also something that you don't want in a Sunday puzzle, a thing that last week's had aplenty.

3. Would inhalable chocolate help us solve this? Listening now. . .

4. I've had Le Whif. It's totally unsatisfying, as you might expect. From the name alone. It's a Frenchified version of a baseball term meaning an attempt to hit it out of the park that misses completely.

1. Paul -- Elegant, as usual! (Your comment, not the clothing.)

2. What a crock!

76. This comment has been removed by the author.

77. I heard the answer to last week - what a crock of ..... Anyway, no issues with this week's challenge.

78. I came up with an answer whereby the second half is definitely something unwanted in clothing, the term is obscure.

For NPR puzzle posts, don't post the answer or any hints that could lead to the answer before the deadline (usually Thursday at 3pm ET). If you know the answer, submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving. You can openly discuss your hints and the answer after the deadline. Thank you.