## Sunday, March 29, 2015

### NPR Sunday Puzzle (Mar 29, 2015): May I Have Your Number?

NPR Sunday Puzzle (Mar 29, 2015): May I Have Your Number?:
Q: This week's challenge is a little tricky. Given a standard calculator with room for 10 digits, what is the largest whole number you can register on it?
I must have misdialed while trying to phone a friend; I got Ed Asner instead.

Edit: I was trying to contact the mathematician Edward Kasner who, along with 9-year-old nephew Milton came up with the name "googol" for the large number 10¹⁰⁰.
A: If you type 706006 (or 709009) and turn the calculator upside down, it spells gOOgOL (or GOOGOL). That's a 1 followed by 100 zeroes and is bigger than any regular number you could enter using 10 digits.

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. As those of you who have been around for a while know, puzzles involving digital numbers are my favorites :) Notwithstanding, I believe I have the correct answer.

Chuck

4. As usual, our genial host says, "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) ." Enough said. ---Rob

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5. K Baine. I get your clever hint - which shows we have the same answer!

6. The greatest PRIME number with 10 digits: 9,999,999,967.

7. Not even going to attempt this one. I only do word puzzles, not number puzzles. I could offer a word puzzle if anyone's interested. Think of a place that's the setting for a well-known sitcom of the past. This place has an A in its name. Drop the A and rearrange the rest to get the nickname of a character working there. Where is it, and what's the nickname? For extra credit, provide the character's actual name.

1. patjberry,
Thank you for posting your puzzles here. They are clever, IMO.

Can you please give a subtle hint for this one? Merci.

LegoNeedSomeSitcomSOS

2. This puzzle is as painless as suicide, and I'm being frank here.

3. The name of the place is kind of in the show's title, just under the radar, you might say.

4. I think it's safe to say that in regard to the character in question, a crony might already have been mentioned, perhaps more than one. Not to mention a linguistic hint at the title.

5. Thanks for the hints patjberry. I had considered this sitcom but was hung up on the trying to make a nickname out of EROK.

Really a nice puzzle. And your hints were very helpful (albeit perhaps a tad too helpful). But, I am not complaining. I asked for hints; you complied. Thanks.

LegoLabdia

6. I tried to offer a clue as well. Perhaps it was not sufficiently spelled out.

7. Tim O.
Your clues were well-placed and clever, but superfluous in the wake of pjb's clues. But your clues did help me also. Thanks.

Leg O.

8. A couple of nice clues so far, especially Blaine's.

I submitted the true mathematical answer (according to my HP) as well as the "intended" trick answer along with a couple of variations of the trick answer. (I know, only one answer per person, but I identified one as my "official" entry.)

9. I have a possible answer to this puzzle, and I have great admiration for Henry Hook’s puzzling prowess.

I would feel better about my answer if I could access one of them nifty Army-base stores, or if I could deep-six my Windows 8 and return to my previous OS. But I can’t, so I don’t.

This is ostensibly a number puzzle. I don’t know much about history, biology, a science book, or how to solve number puzzles by Henry Hook. But I know this much: There are a few half-way decent word puzzles on this week’s Puzzleria!

LegoLaudsHenryTheEighth…WonderOfThePuzzleWorld

10. Think outside the box on this one, read the original puzzle closely for 'gotcha' wording.

11. I wonder how many people will come up with the right idea - but be graded incorrect on a technicality.

12. I wish it were easier to look this one up on the internet! -- Margaret G.

13. I got the answer thanks to a hint on here...but there are other hints on here that baffle me in relation to the answer! I can't wait for next week when everyone can reveal what they mean!

14. Took me longer to get Will's intended trick answer, but I think my first answer is mathematically legit and bigger (and for once I get Blaine's clue - yay !)

15. I've got a plenty big 6-digit answer, but I can't get my 10-digit answer to work on a "standard calculator".

1. Questions abound about the significance of "standard calculator."

2. I think many may duck giving an answer this week, especially given the upcoming Easter holiday.

3. Claire,
Thanks for chiming in/piping up. Don’t worry, many of us (and even Will Shortz himself!) have gone on record admitting we often don’t understand Blainesvillians’ clues, even when we know the answer.
BTW, on Blaine’s blog we can reveal our answers and clues/hints every Thursday at 3 PM Eastern Time.

Dave Taylor,
I wish I were as clever a solver as you. (I’m serious.) I think I have your first answer but I am still in the dark about Will’s trick answer and Blaine’s clue. Perhaps I’ll have to wait till Thursday for that Aha!-Hit-me-over-the-head-with-a-hammer moment.

jan,
I believe I may have alluded to your ten-digit answer quandary in the second paragraph of my Sunday 4:45 PM post?

WordWoman,
I am familiar with standard deviations, standard deductions, and even Standard Oil! I guess I am not familiar with standard calculators.
As to the Easter holiday: yes I agree that the correct entry total will be lower, thwarting Will’s recent successful attempts to goose those totals.

Lego*perplexed

4. @Lego Lambda - I think a STANDARD calculator is differentiated from a SCIENTIFIC calculator, in that is has less keys and can only display the digits 0-9 on a simple 7 segment LED display, i.e. no complex math (sort of).

5. Dave Taylor,
I read the puzzle again before retiring last night (I’m looking forward to collecting my pension!), and this morning the "tricky" answer popped into my head. Aha! Finally!

I assume I now have in my possession the trick answer that had been already sussed by you, Blaine, Lorenzo, Jim, possibly Chuck and 68Charger and who knows how many others.

But don’t you think Will will still have to accept all those non-9,999,999,999 answers that very arguably also are “a little tricky”?

16. So why isn't it just all the nine's you can cram on there? Or is it meant to be expressed in terms of X times 10 to the 8th power or something?

1. I don't think anyone would consider 9,999,999,999 to be "a little tricky".

2. Well maybe that's the trick, jan! (just kidding)

3. Take a trip to the Children's hospital, UJ. Remember the original name?

17. OH, maybe I've got it all topsy-turvy.

18. 69? Sounds dirty.

19. What's the difference between the answer and a Russian writer? Nothing.

1. Clever.

2. jan,
In a manner of speaking.

I love your clue and have been thinking of this author, but did not get creative with it. Bravo!

3. The missing link, so to speak.

20. For problems like this I always turn to my son - LEO BIBLE

21. Not A Clue: I believe there is only one other value that may be displayed on the calculator that exceeds the answer. Can anyone prove this wrong ?

1. The only value greater than Googol is Infinity, which is represented by the 8 symbol rotated 90 degrees. (Yes, this is valid according to the Shortz Wonderland world of upside down digital clocks and calculators.)

2. I thought of infinity via 8 turned ninety degrees, but many searches online insisted infinity is NOT a number, so I discounted it. I still like it though.

22. I'm going with 80085 :)

1. Not 5318008?

2. David, are you trying to titillate us?

3. First that Australian woman who's been flashing the Google StreetView car, and now these two flashing a Googol puzzle...

23. 9888888886

If you assume that the calculator will only be viewed in its standard vertical orientation – i.e., right side up – then the obvious answer is 9999999999. However, that would not be the answer if the calculator were held upside down. 9888888886 is the largest number that works holding the calculator right side up and upside down.

Chuck

24. Enter "706006" and turn the calculator upside-down to read "googol" (10 to the 100th power).

> I've got a plenty big 6-digit answer, but I can't get my 10-digit answer to work on a "standard calculator".

I can't see how you can get "googolplex" with 7-segment displays.

> What's the difference between the answer and a Russian writer? Nothing.

GOOGOL - GOGOL = O.

I thought Blaine's "Ed Asner" clue was brilliant, if completely unhelpful.

25. GOOGOL by typing in 709009 and turning calculator upside down

I couldn't find a way to make GOOGOLPLEX work because of the X. A googolplex is somewhat larger than a duplex.

26. GOOGOL or, even larger, 9999GOOGOL

Both answers above are upside down on a "standard" calculator.

"I think many may duck giving an answer this week, especially given the upcoming Easter holiday." referred to the OTHER search engine Duck, Duck, Go.

1. As with 999 thousand, for example, I think a space is required for multiples of a googol. So 999 googol was the best I could do with a 10-digit display.

2. Yet, Lorenzo, in crossword puzzle-eze (or ease if you prefer), the number and word are smushable.

27. The best I could come with was to enter 3333333333 Invert the Display to read`EEEEEEEEEE then convert from Hexadecimal to Decimal

28. I went with 7060066666 which gives 9999googol.
Mamaw Creek went with 4017716006. The 4 with artistic license could be an 'n.' This leaves us with googillion, astronomy's largest number.
Zeeeeeee...ke

1. But is a googillion a whole number? Citation needed.

2. At the risk of seeming presumptuous we were thinking that the sum of everything would be the whole.

3. Ay, Gestalt!

29. If its all the same to the rest of you, I like 72

1. This strikes me as the most innovative answer so far. Care to elaborate?

30. I should take a solemn vow never to answer another upside down alarm clock puzzle for the rest of my life. I just don’t do well with them.

In an interesting matter but unrelated to this week’s puzzle, I got an email from Will Shortz this morning. Though he and I have corresponded before, I felt confident it was not really from him so I didn’t open it or click on the link contained therein. I guess someone has hacked one of his email addresses.

Has this happened to any of you?

Chuck

1. We're really not that close. ;-)

2. Wouldn't 42 be the #?

3. Wouldn't 42 be the #?

31. I considered suggesting 8888888888: Turn it on its side, and you've got ten infinities. Beat that!

1. Although, as with googillion, jan, can you prove definitively that any amount of infinity or infinities is a whole number?

2. Me, neither. I think it will be interesting to see if Will goes with googol or 9999googol.

Or something else, of course.

3. jan,
Your sense of humor seems endless.

4. hahahahahahahahahaha ... where'd you go?

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33. I honestly did not see GOOGOL coming. Turned out it was also a word puzzle after all. BTW the answer to my puzzle is HOSPITAL and HOTLIPS(Maj. Margaret Houlihan). M#A#S#H stands for Mobile Army Surgical Hospital. Thanks to Legolambda for the compliments.

1. The movie and TV franchise was M*A*S*H. I'd say that M#A#S#H should be pronounced "mashtag".

2. Sorry but I can't deal with all these Mashinations.

3. If M=13, A=1, S=19, H=9, and *="to the power of'" , I don't even want to think about it; and if I've made a translation error, I certainly don't want to think about that

4. Anyone know why they used asterisks instead of periods in the M*A*S*H title?

5. WW
I've always assumed it was for historical accuracy.

6. The movie cost a lot to make and it was their *.

7. I figured it was just artsy since there is no * after the H.

8. And 13*1*19*9=a trivial 2223. What was I thinking?

9. Sorry, I didn't see the asterisk button. Clearly I meant M*A*S*H. I don't know why they used asterisks either. Or should I say *s? Or is it *'s?

10. What else could I say about my puzzle other than Swit happens?

34. The mundane answer, not the one I submitted: There is “ROOM” for ten numbers, but, in fact, only eight numbers can be entered. So the answer is 99,999,999. or 8 nines. If you add 1 to this number, you receive E(error) + space + 1.0000000 or a total of 8 slots for registering numbers and 2 extra slots for registering E (for error) + a space.  This means there is  “room” for ten numbers, but only eight numbers can be entered. The decimal point does NOT count or occupy a full space.

There is another, certainly the intended, solution: The “trick” is to remember that digital numbers can stand for letters, so the answer is: googol, which is 900901 (or an upside down 106006 or 706006) on a digital calculator display. (Chuck should appreciate this puzzle!) GOOGOL is the number 10^100 or 10 to the 100th power, a 1 followed by 100 zeros! This is surely the largest number possible on a calculator display with “room for ten digits!”

My hint: 4615, an upside down digital “sigh.”

Yes, if you add an O (or zero 0), which is “nothing,” to the Russian author, Gogol, you have googol.

1. I also noticed on my two old calculators that there is room for ten digits on the display, but only eight register. I thought that might be the trick at first.

2. Just enter 900901 and digitally that is googol; no need to turn the calculator display upside down!

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4. There is also 9999009015 = digitally 999 googols with 10 numbers entered!

5. 1, digitally, is a lower-case l (ell), and just as 9 is a lower-case g. So 1 can represent either a lower-case l (ell) or a capital I (eye).

6. I like it, ron, but am not sure you need the 5 at the end and could add another 9 at the beginning. We would more usually say 9999 million, rather that 9999 millions, eh?

7. Googol is not a denomination like "thousand" or "million." It is the name of a specific number like 2 and you would say ten twos.

35. I'm concerned that we may all have missed this one. "Googol" would be a good answer if the calculator had room for just 6 digits, but if it's right, that 10-digit limit seems irrelevant. Did anyone else consider the 10-digit calculator that's always handy, and think that 10 is the highest number we can count to on our fingers?

1. Leader-in-the-clubhouse candidate for Blainesville 2015 Description of the Year Award:
“Yes, (infinity read as a sideways 8) is valid according to the Shortz Wonderland world of upside down digital clocks and calculators.” (xfyre’s Thu Apr 02, 12:15:00 PM PDT comment)
Leader-in-the-clubhouse candidate for Blainesville 2015 Word of the Year Award:
“smushable” (Word Woman’s Thu Apr 02, 01:04:00 PM PDT comment)

My first stab at this wonderful Henry Hook puzzle yielded 4017712999 (999 zillion) or 4017718666 (999 billion). But I was uncomfortable with “inverted 4 = n” because, really, with “inverted 4 = h.” Nor was I thrilled with “inverted (or uninverted) 2 = Z.”

Then I remembered googol and googolplex, which I misspelled google and googleplex. (It will be interesting if Will accepts 376006 or 376006666 as answers. He shouldn’t, of course (As SuperZee commented, they might “be graded incorrect on a technicality.”), But still, Will might be in the mood to muster some Holy Week compassion.)

I looked up google in my Merriam Webster’s Collegiate Dictionary Tenth Edition and found “googly-eyed,” with googol and googolplex beneath it. These correct spellings also inverted nicely into numbers… except for the “x” and “p” in googolplex, to which I alluded in my comment which included:
“I would feel better about my (inverted) answer if I could access one of them nifty Army-base stores (PX stores), or if I could deep-six my Windows 8 and return to my previous OS (Windows xp). But I can’t, so I don’t.”

Oh how I so wanted GOOGOLPLEX to be the answer. It takes up exactly 10 spaces and it is pretty much the largest number short of infinite. “Can an X variable be registered on some standard calculators?” I wondered. Even if so, there was that pesky “P.”

BTW, my MWC Dictionary 10th Edition defines zillion as “an indeterminately large number” and infinity as “an indefinitely great number.”

However, I did not submit 999BILLION, 999ZILLION, 9999GOOGOL OR, ALAS, GOOGOL?LE? am my answer this week. I submitted another answer, one I believe is Henry Hook’s and Will’s intended answer. It is one of those whole numbers that loses value when you invert it.

I will reveal the anser I submitted on the new Puzzleria! blog, which I will upload Friday morning, April 3.

I just now read jan's comment. He scooped me. Still, I will cuss my answer on Puzzleria! tomorrow.

...0637

2. I am not sure count is the same as "register".

3. I'm not sure anything is the same as anything. Wanna join my club?

4. I didn't get the call, today, so the belief in my intended answer may be unfounded. But after Chuck's 12:47 PM comment today, perhaps Will/NPR is now e-mailing instead of phoning.

LegoLoser

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7. Which do you prefer: a puzzle where we're wondering where anything is the same as anything or an Aesop's Fable/Jamie Lee Curtis type puzzle?

8. At this point in my life, I don't prefer waking up in the morning.

But I like to think I'll always prefer wonder.

I always prefer wonder.

9. Paul,
I wanna join your club. What do we call ourselves, the Anti-Synonymites?

LegoSomething/Anything?

10. Of course, if *="times", I'm full of shit, but it doesn't stop me from wondering.

11. Lego-Thanx for picking up on my Googol vs Google "technicality" comment.

12. Lego, been thinking about googolplex. How about switching to Roman Numerals for the last digit ;-)?

13. You are welcome, SuperZee. 'Twas an astute comment.

Word Woman,
Yes. The idea of a Roman numeral calculator did cross my mind during the solving process. Boy, I would love to see the circuitry inside of that baby! Bot binary. Not base-10. Base-Alphabet Soup!

36. The wording of the puzzle leads one to look for a 10 digit answer.

37. I knew this might have been completely wrong but I thought why not make it a plane number "8"? Turn it sideways and it's the symbol for "Infinity". Oh well, I knew it was an outside chance.

38. Like many of you, I went a little 'googly' over this puzzle myself.
* I thought 'googol' was a good answer, and saw several clues towards it, but the 6 (vs. 10) digits bothered me. That would be unnecessarily 'tricky,' because there'd be 3 (or at least 2) 'tricks' involved: spelling, inversion, and not using all the characters.
* "8" should be out, as infinity is not a whole number...A philosophical debate might have ensued if the word 'whole' weren't there.
* "Register" instead of "display" had me thinking too much about internal calculations, or other meanings of the word...
* LL, your clues pointed me to consider further, past googol (and even googolplex), and I really wanted something with finger counting to work. In fact, I thought Blaine's clue 'pointed' to the character "Mr. Finger."
So I considered numbers like 10, 55, and 2^10. Some people suggest that we can count to 3^10 on our fingers, if we are clever and adept at having our fingers half-raised.
I am not, preferring to fully extend -- and then dismissed that possibility.

So I like 'googol' the best, but frown upon the extra 4 digits. Prefixing "9999" makes logical sense, but either option makes the puzzle less elegant, IMHO. Cheers, puzzlers!

39. I submitted 6666666636. Upside down this is 9E99999999, or 9 times 10 to the power 99999999. This is bigger than googol, which, embarrassingly, I didn't get. It will be fun to hear Will's comments!

40. 0 is the largest hole number.

41. Couldn't you actually put "8888" at the end of 706006 so you get 8888 googol?

1. Or to answer my own question end it with 6666 and get 9999 googol?

42. As many fellow Blanesvillians (Blainiacs?) did. I started with 709009, inverted to spell GOOGOL - then "upped the ante" to 7090096666 inverted to make 9999GOOGOL and I submitted this as an answer.

However, as I looked at my calculator, I remembered that the letter E (an upside down 3) can ve used to indicate exponentiation. Thinking of the GOOGOLPLEX I began to type an entry as 7090093666 intending it to be read as 999^GOOGOL. However, as I began to type this I realized that 9^9 is 387,420,489 and is much larger than 999 so my final submittal was 7090093636 which inverted is 9^9^GOOGOL.

As I too wasn't called by Will, I have no idea if he accepted this answer...

We'll see what Will says on Sunday.

1. SuperZee, I considered the exponents answer but decided that function would most likely be on a scientific calculator not a "standard" one.

And, yes, we'll see on Sunday. Meanwhile, it's been fun.

43. Left Shark
6666666636 >9E99999999
or 9 followed by 99,999,999 zeros

1. Clue was 12983, largest prime factor of 6666666636

44. Edit: I was trying to contact the mathematician Edward Kasner who, along with 9-year-old nephew Milton came up with the name "googol" for the large number 10¹⁰⁰.

That won't be too easy as Kasner dies on Jan. 7, 1955

45. died, not dies

1. Right! It would not be fair to have him have to go through that again. Who knows where that would lead to and when it would stop? Why it could go on into infinity.

46. Blainesvillians (or, Blainiacs, courtesy of SuperZee's cleverness),

ACCOMPLISH some fun today! A Creative Challenge On My Puzzleria Link Is Sheer Heaven!

Lamb'sEyesGraze(sic)Over

47. SuperZee,

I also submitted 9E9EGOOGOL (enter 7090093636). Glad to see that someone else came up with the same answer.

Regards – Phil J.

1. Nice to know I wasn't the only one to go there. Whether Will calls it right or wrong, we have each other as validation.

48. I think we have to be somewhat realistic here. Even though listeners to NPR tend to be more intelligent and well informed than the majority, I don't think most will have even heard of googol. This is a puzzle for the masses, so to speak, and therefor I doubt very much it will have been complicated to make the answer more than GOOGOL. Several here have posted well thought out and intelligent ways of increasing the number to an even higher answer, but I think that misses the intent of the puzzle, which is to find googol by creatively using the keypad and then turning the computer upside down. Anyway we will surely find out soon when my clock radio comes on at 9 AM and hear Will Shortz explain the intended answer, along with what I hope he will also accept as close enough to qualify. That assumes my radio will even come on in the morning since it is still turned upside down.

49. For the record 8888888888 is a number with 20 holes. That's pretty large.

50. Next week's challenge: Name something that might be worn on the foot. Change one letter in it without changing the order of the other letters. The result will name something one might wear on the upper part of the body. What is it? Here's a hint: The thing on the upper part of the body is a two-word phrase.

51. I have a mole on the upper part of my body, and I think a hint should be a hint and a constraint should be a constraint.

52. I just heard the answer to last week's puzzle. I was wrong about the "hands = calculator" answer. I had a hunch. I was dead wrong, just as I was wrong about last autumn's "four clock-times" puzzle which I thought was "FALL BACK" was was really "the hands resemble the Roman numerals C, I, V and L."

BTW, I think Will said he would accept GOOGOL and 999GOOGOL, but not 9999GOOGOL. What's that about?

1. What I thought Will was saying was that he accepted all the variants of X times Googol. Even so there were only some 200 correct answers.

2. Perhaps multiples of googol are not smushable after all!

53. If you go to Wikipedia, enter the <something that might be worn on the foot> into its search engine and click, you get "<what you typed> may refer to:", then two examples of what you typed - only neither of those options may be worn on the foot - then an alternate SPELLING of what you typed - but you can clearly see that THAT is the option you must select.

Then you see "A <the alternate spelling> (or <YOUR SPELLING>) is a ..." and conformation that you indeed have the correct answer; only Wikipedia prefers the alternate spelling.

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1. I didn't have the answer when i posted that comment.

55. 106006 should also work.

For this week, the answer came fast enough that I think I must have heard the answer before. Or at least half of it.

56. With the half of a repeat answer I felt like kicking myself when I finally figured it out.

57. Literary fragment spoonerized.

I'm getting "tired" of repeat puzzles.

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60. I was out on my bicycle, getting a little exercise, trying to lose my fat butt, when the answer came nigh to me. Hope I win the prize. Is four clues enough?

1. Missed one. Five clues.

61. I walked past a shapely person like that earlier today. But she wasn't exercising.

62. I've come up with a solution - but it doesn't seem to fit any of the other clues. I'm afraid that when I share it with you all on Thursday you'll make fun of it.

63. I'm not sure if this is saying too much, but I made three of these in the last eight days.

64. I spoonerize at least two of the uppers on my lowers per day, Lorenzo.

65. What happened to Blaine? Is he still out looking for his eggs, or what?

66. As often happens, I heard the challenge at 8:40 AM, thought about it, tried some dead ends, got nowhere. Then I heard the re-broadcast at 10:40 (today I was on the highway driving to my sister's house for Easter dinner) and got the answer immediately.

The foregoing is a true story and contains no hints.

I did consider posting a movie-related hint, but that could be a giveaway to some people.

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.