## Thursday, August 22, 2013

### NPR Sunday Puzzle (Aug 18, 2013): Roman Numeral XXXVIII

NPR Sunday Puzzle (Aug 18, 2013): Roman Numeral XXXVIII:
Q: The Roman numeral for 38 is XXXVIII. What is special or unusual about this Roman numeral that sets it apart from every other Roman numeral that can be written?
I'm sure I'll figure this out next month when I go to New Jersey.

Edit: If you sort the months alphabetically, September comes last. Similarly, if you sort the state capitals, Trenton comes last
A: XXXVIII sorts last alphabetically.

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. Before settling on your answer, consider these numbers: 88 = LXXXVIII and 888 = DCCCLXXXVIII. The longest word that can be made from the letters used in Roman Numerals is 1602 = MDCII = IMIDIC or 1402 = MCDII = IMIDIC. See: http://dictionary.reference.com/browse/imidic?s=t

There are several 5-letter words that can be made from the letters used in Roman Numerals: MIMIC, CIVIC, CIVIL, LIVID.

1. I meant 1603 = MDCIII and 1403 = 1403 = MCDIII both anagram to IMIDIC.

2. XXXIX and CCCIC messes it up.

3. 39, XXXIX and 399, which is CCCXCIX, NOT CCCIC messes what up???

4. Sorry, I went with a different direction on that one.
Old rabbit hunter Zeke.

5. lexicographically?

6. IC is not a correct Roman Numeral. Nor is IM. You do not do 1 below any numeral but V and X. I teach Latin and KNOW Roman Numerals. Romans mor often than not used IIII for 4.

7. Neil, besides that IC would be totally ICKY, unless reserved for ice cream. . . There is something stately about them that gives one pause. Maybe that was the founding fathers ideas when they put Roman Numerals on the Great Seal of the United States.

In any case, weLCoMe.

3. What's the long of it?

4. I have an answer but it’s so trivial the question hardly seems worth asking :(

Chuck

5. Interesting words, regarding some famous people, from some fellow bloggers at the end of last week's blog.

6. Ahh, I woke up from my zzzz's this morning to listen to the puzzle and realizing we are almost at the end of summer. Then a fitting Donna Summer song kept playing in my mind. . .

1. Yes, the last of the sweet, juicy Colorado peaches are arriving from Palisade. And my daughter ends her teen years on Tuesday. This time of year always stuns me with the hint of fall in the night air.

2. Or, our darling XX is XX today.

7. Tyler Ferrar knew the answer, then he forgot.

8. As Heywood Banks would say, there's 18 wheels on a big rig, count them I II III IV V VI...XV XVI XVII XVIII and they're rolling rolling rolling...

9. 38 is an interesting number. On the other hand 100 is too.

1. Just wondering:
are 3,053 and 3,800 interesting, too?
Or do I have the wrong end of the stick?

Orangebus

2. Not nearly as interesting, Orangebus. Not sure about the stick.

3. Orangebus: Your two numbers are more or less in the middle of the stick.

4. At the time, I was going with the first thing I noticed, that all the letters in XXXVIII were in reverse alphabetical order. Of course, so are MMMLLLIII and MMMDCCC.

This notion seemed to be supported by these sequences in Blaine's hint:
out next month
when I go
to New Jersey.

And so it goes.

1. Oh, I see!

2. Officer In Charge of just what?

3. Just produce zee letters, old man.

10. The following is an elaboration of what I posted at the end of last week's blog:

Does anyone notice what James Fenimore Cooper, Mitt Romney and custom, hand-made shoes have in common with this puzzle?

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2. The best I can do is notice that JAMES FENIMORE COOPER, WILLARD MITT ROMNEY, & GRAVATI CUSTOM HANDMADE SHOES contain the letters: ROMAN NUMERAL FOR THIRTY EIGHT.

3. That is interesting, but not really a clue. My clue, when I last checked, is a real hint.

11. "Special or unusual?" Whenever I find Will's clue and the posts on this blog obscure and head-scratching, I figure it's directed to a part of the brain that I either don't possess or that has been compromised by too much Merlot over the years, so I will simply wish you all a great week and I'll check in again on Thursday afternoon.

12. I truly haven't got the slightest idea what this puzzle is getting at, and this week all of your hints and commentary haven't helped me a bit.

So I'll throw out a very minor puzzle that occurred to me while I was doing a crossword puzzle recently. (As far as I know, this is original to me, but it may have been used before.) (And, yes, I realize that you will have solved it at about the same instant I hit the "Publish" button.)

"Think of a word meaning "foolish". Add an "S" and you will get a word that can be taken to mean even more foolish. What are the two words?"

1. Anagram or somewhere to the original order?

2. Kefufflesan,
I consulted my daughter about your puzzle but Annie's expertise did not cut the mustard.

3. I got it right away, but I won't post the answer.

4. Insane and inane.

5. With the cat out of the bag Annie's was my anagram of the answer plus s.

6. And if the latter happened in Paris, it could be "in Seine."

Cutting the mustard and letting the cat out of the bag, Zeke Creek? I guess that's better than mixing those two sayings.

Ruth and Bob, using Roman Numerals as a beginning way to explain some terms in Algebra to elementary and middle-school might help. Or not.

7. Thanks for the attempt, WW, but my brain just absolutely refuses to get the hint. I shall await Thursday at 3 PM!

8. Last clue: only seven letters make up all Roman Numerals...

9. Roman numerals is more like counting sticks. If you have only x number sticks to work with then you can only derive so many answers.

11. WW - Yes, indeed I am. Was hoping I would be able to call the solution bogus, but it is rock solid. I was thinking of all kinds of numerical properties, never considered the spelling. I find, in my current daze (all of yesterday was taken up with the funeral of a 104 yr old friend), that I have been considering that even if you counted to infinity in Roman numerals, then re-arranged the numbers alphabetically (could be some technical difficulty there) you know in advance that the last member of the set would be XXXVIII. Not sure if that means anything.

12. I've been shaking my head all week and have the dizziness to prove it. I truly do not get this puzzle or even Blaine's answer. "Sorted last alphabetically" means exactly what? Even Word Woman's patient explanation leaves me stymied. How is XXXVIII is the last alphabetically? The last what? Sigh...

13. Ruth - As WW pointed out, and I completely missed at the time, there are only seven Roman numerals, I, V, X, L, C, D, and M. If you consider the numbers made from these letters to be words, and then arrange them alphabetically as word-like constructions, the first will necessarily be C, and the very last must be XXXVIII, because X is the last letter alphabetically in the set, and the maximum number of times it can be used at the beginning of a number is three, and V can only appear once after the three Xs, and three Is is the maximum allowed, and the only numeral that can appear in that position.

14. Ruth:
Think of XXXVIII as an actual word and then try to figure out exactly where you would place that word in a dictionary. Maybe that will help you understand.

15. Bob, I am sorry to hear about your friend's passing at CIV.

Ruth, go to Barbara H's output below. You will see the Roman Numerals arranged alphabetically.

The lack of a zero as a placeholder really did in this system. But I can see IIII with a diagonal line across it becoming V, and two opposing diagonals / and \ becoming X...Isaac Asimov proposed that the Romans preferred IIII to IV because IV referred to the god Jupiter.

Using Roman Numerals on clocks seems quite odd to me as the numerals seem so easily confused when they are written in a circle. Some propose another reason the Romans preferred IIII over IV is because IV and VI are too easily confused. Must have been tough for those with dyslexia. I tutored a 24 year old man with dyslexia and he said our Arabic number system was so much easier to keep straight than our alphabet.

13. f(decimal) = g(Roman) for decimal = Roman
Well, maybe it's unique for this puzzle. But I think the definitions of f and g are persnickety.

1. And Lemon-y.

2. I knew my definitions of f and g overspecified things:
f(decimal)="the letters in"(thirtyeight)=11
g(Roman)="the chisel lines in numbers<XL"=11

\\\///\/|||, and certainly doesn't work if puzzle posed in German.

14. XXXVIII -

The Patriots won.

Chuck

1. ...barely beating the Carolina Panthers, who went from last place in their division the previous year to first.

2. Thank you, Bob K.

15. And wardrobe malfunctioned.

1. My towel is downstairs. Thanks for asking.

2. Every hoopy frude...

1. What is VI * IX ?

2. LIV (ULLMAN or TYLER).

3. Will u still need me? Will you still feed me when I'm XLIV?

4. Hey RoRo, sure...but you are much younger than Sir Paul! :-)

5. True true when last I checked

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17. How to beat Will at his own game.

That one friend... / iFunny :)

http://ifunny.mobi/p/D6GswEXH1

Go back one clip to "That one friend..."

18. Besides whatever else may be so, 38 is the lowest number that can be written using 7 Roman numerals.

Chuck

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20. XXXVIII is the LAST Roman Numeral written alphabetically.

My Hint XXXplained:

"Does anyone notice what James Fenimore Cooper, Mitt Romney and custom, hand-made shoes have in common with this puzzle?"

LAST is what they all have in common. Cooper wrote "The LAST Of The Mohicans." Mitt Romney LOST his race for the White House by coming in LAST. Hand-made shoes first require a LAST be made of each of the customer's feet.

1. I got the answer and the Cooper and shoemaker references, but the Romney reference confused me. He actually came in second out of 20-something presidential candidates that got on some ballot somewhere. The Libertarians, Greens, Constitution Party, Whigs, etc., etc.

2. I have to agree with you abut Romney. I was looking at it from the standpoint that there were realistically only two candidates. Had I thought about the other losers I probably would not have included that creep in my hint.

3. Yeah, I was wondering how Romney fit in among 2 other good hints...kinda weak! ;)

4. Right! That's why he lost—kinda weak! :)

21. I noted the LAST of the Palisade peaches and the END of my daughter's teen years on the XX of August when she turned XX. All were references to XXXVIII being the LAST Roman Numeral written alphabetically.

This was one of my favorite puzzles of the summer.

22. Repeating my hints above, when sorting alphabetically September is the last month and Trenton, NJ is the last state capital.

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24. I fail to see the answer to the puzzle...I was able to come up with a hexagon using the numbers from 1 to 19 that on the diagonal(outside) and across all total 38.
Please explain Will's puzzle to me. and ty.

1. Consider the Roman Numerals as the letters that they are. C is the first numeral alphabetically and XXXVIII is the last alphabetically. 39 is XXXIX which precedes 38 alphabetically. 40 is XL and so forth. 38 has the maximum number of XXX followed by a V and III. So it comes in dead last. Hope that helps.

25. My Submission: Any three letters of XXXVIII can be multiplied together to get one of the letters of the Roman Numeral system: I, V, X, L, C, D, M. Each of these 7 letters can be obtained by the product of 3 of the letters of XXXVIII, and no other number except these 7 can be obtained by such a product. For example, X*X*X = M, X*X*V = D, X*X*I = C, X*V*I = L, X*I*I = X, etc. There is no other number besides XXXVIII for which this is possible.

26. XXXVIII is the last Roman numeral in which the letters used to make the Roman numeral are included in all the previous numbers going back to the number one. Perhaps it will earn honorable mention.

27. Just for fun, to see the numbers, run this Python program http://nickm.com/poems/first_m.html, or view its output, the first M numbers in alphabetic order, here http://nickm.com/poems/first_m_output.html.

1. Barbara H., thanks for these links. I sent them to my math major son in Australia and he was intrigued. A great, think outside the box puzzle!

Ruth, lgo to the second link and you will see. . .

28. Lexicographically, the last string which represents a valid Roman numeral.

29. My post: "Interesting words, regarding some famous people, from some fellow bloggers at the end of last week's blog" included the words "famous last words" which was a reference to the fact that 38, expressed roman numerically, is last alphabetically.

30. My post: "38 is an interesting number. On the other hand 100 is too." referred to the last and first Roman numerals when listed alphabetically.

31. This reminds me of a couple of jokes I made up some time ago:

I bought a can of alphabet soup once and considered myself a man of letters.

Once I was dining on a bowl of alphabet soup in a posh bistro and complained to the waiter that there was a fly in my soup. He correctly pointed out that it clearly said ant.

32. It's nice to come up with some sort of alphabetical puzzle, but Roman numerals are Roman numerals and not Roman letters.

1. Many of the Roman numerals were added to the Latin alphabet rather than the Latin alphabet becoming Roman numerals.

33. By the way, some of you may be interested in the Number Gossip website, for collected unique properties of numbers.

An example for 38:
Unique Properties of 38
38 is the magic constant in the only possible magic hexagon (which utilizes all the natural integers up to and including 19)
XXXVIII (=38) is lexicographically the last string which represents a valid Roman numeral
38 is the largest even number which cannot be written as the sum of two odd composite numbers

In fact, a google search of "38 roman numeral" leads to that page on the first set of results(!)

1. yes that's what I wrote just above

34. Another interesting property of 38 is that the number of pen strokes needed to write it as a Roman Numeral (sans serif) is the same as the number of letters needed to spell it in English. I think there are seven other numbers that share this property.

1. ...AND... the digits themselves add to that very same number (of strokes and letters)!

2. I've found nine other numbers that share that property, thanks to the fact that 3084 and 3089 both have their names spelled with 23 letters and have their Roman numerals written with 23 strokes.

#letters = #strokes for 6, 8, 30, 36, 38, 81, 83, 3084 and 3089.

#strokes = Sum of digits for 36, 37, 38, 40, 41, 42, 43, 80, 81, 82, 83 and 1088.

#letters = Sum of digits for 4, 16, 36, 38, 54, 62, 70, 74, 81 and 83.

#letters = #strokes = Sum of digits ONLY FOR 36, 38, 81 and 83.

3. Sorry, make that eight other numbers sharing that property besides 38.

4. ACHHHH! Ok, forget my previous posts. It was nine other numbers besides 38 having #letters = #strokes. I had forgotten 85, and also 50 in the #letters = sum of digits catagory.

#letters = #strokes for 6, 8, 30, 36, 38, 81, 83, 85, 3084 and 3089.

#strokes = Sum of digits for 36, 37, 38, 40, 41, 42, 43, 80, 81, 82, 83 and 1088.

#letters = Sum of digits for 4, 16, 36, 38, 50, 54, 62, 70, 74, 81 and 83.

#letters = #strokes = Sum of digits ONLY FOR 36, 38, 81 and 83.

5. ...And still my lists were not complete! 3082 has its name spelled with 22 letters and its Roman numeral is written with 22 strokes, so it's ten other numbers besides 38 having #letters = #strokes. Also 45 should be included in the #letters = sum of digits category.

6. Wow! And I thought I was obsessive! :-)

7. Ward, that was where I was going at first til the clues and my HS memory led me at last to the intended answer

35. I can't believe it. The new puzzle has been up for a few hours now, and still no one has posted here?

Well, anyway, here it is:

Next week's challenge: Think of a business that's found in most towns. Its name consists of two words, each starting with a consonant. Interchange the consonants and you'll get two new words — neither of which rhymes with the original words. What business is it?

1. To those who might wonder "Any relationship between the new words to the original words, or to each other?":

I don't think one would feel <2nd new word> if he or she were to find him or herself unexpectedly in the midst of a <1st new word>.