Sunday, October 19, 2014

Hint: It's a REGULAR Grade School Classroom

Before I get to this week's puzzle, a word about the Country - Capital - Country puzzle from last week. Interesting that three of our four answers were allowed by the Puzzle Master. As Ross commented, Will Shortz must have disallowed Aruba, which "is a country the way Scotland is a country--it's a sovereign territory." Fair enough, Puzzle Master. I'm sure the nice peoples of the Solomon Islands cheered when they heard your shout out to their capital, Honiara!

Here's this week's NPR Sunday Puzzle:
Out of a regular grade school classroom, two students are chosen at random. Both happen to have blue eyes. If the odds are exactly 50-50 that two randomly chosen students in the class will have blue eyes: How many students are in the class?
I think this takes some paper and pencil. Oh, and this handy list of children's names in alpha order:

Abigail                               Kevin                           Uriah
Billy                                   Laura                           Vanessa
Carol                                  Maureen                      Willie
Diane                                 Nick                            Xerxes
Eddie                                 Olive                           Yancy
Fred                                   Petey                          Zenobia
Gladys                               Quincy
Hector                               Richie
Imogen                              Sally
Jane                                   Ted

We have an answer, which we haven't bothered to prove is the only answer. I trust Martin Gardner did that in the first place. Oh, and if you want a much harder puzzle, check out this blue-eyed monster over at XKCD.

Oh, and don't forget to send in your answers using the gray-eyed Contact Us form right here.

Let's see what Flickr has for HONIARA...

Time for

This is where we ask you how many entries you think NPR will get for the challenge above. If you want to win, leave a comment with your guess for the range of entries NPR will receive. First come first served, so read existing comments before you guess. Or skip the comments and send an email with your pick to Magdalen (at) Crosswordman (dot) com. Ross and I guess last, just before we publish the Thursday post. After the Thursday post is up, the entries are closed.

The winner gets a choice: they can receive a puzzle book of our choosing or they can ask that a charitable contribution is made in the winner's honor. As of this week, we are providing an alternative to the Red Cross. If the winner wishes, we will make a contribution to his/her NPR station. Send us the call letters and we'll do the rest.

I won this week, with 500. So let me ask many people will want to work out the maths for the blue-eyed puzzle?

Here are the ranges:
Fewer than 50       
51 - 100
101 - 150
151 - 200
201 - 250
251 - 300
301 - 350
351 - 400
401 - 450
451 - 500

501 - 550
551 - 600
601 - 650
651 - 700
701 - 750
751 - 800
801 - 850
851 - 900
901 - 950
951 - 1,000
1,001 - 1,050         
1,051 - 1,100
1,101 - 1,150
1,151 - 1,200
1,201 - 1,250
1,251 - 1,300
1,301 - 1,350
1,351 - 1,400
1,401 - 1,450
1,451 - 1,500

1,501 - 1,550
1,551 - 1,600
1,601 - 1,650
1,651 - 1,700
1,701 - 1,750
1,751 - 1,800
1,801 - 1,850
1,851 - 1,900
1,901 - 1,950
1,951 - 2,000
2,001 - 2,050
2,051 - 2,100
2,101 - 2,150
2,151 - 2,200
2,201 - 2,250
2,251 - 2,300
2,301 - 2,350
2,351 - 2,400
2,401 - 2,450
2,451 - 2,500

2,501 - 2,750
2,751 - 3,000
3,001 - 3,250
3,251 - 3,500
3,501 - 4,000
4,001 - 4,500
4,501 - 5,000

More than 5,000
More than 5,000 and it sets a new record.
Our tie-break rule:   In the event that a single round number is announced with a qualifier such as "about" or "around" (e.g., "We received around 1,200 entries."), the prize will be awarded to the entrant who picked the range including that precise number, e.g., 551 - 600 wins if the announced range is "around 600." We retain the discretion to award the prize to an entrant who picked the adjacent range (e.g., 601-650) if that entrant had not already won a prize. In the event that both entrants had won a prize already or neither had, then to the earlier of the two entries on the famous judicial principle of "First Come First Serve," (or in technical legal jargon, "You Snooze, You Lose").  As of January, 2014, this rule is officially even more complicated than it's ever been, but at least it's consistent with what we actually do..


Word Woman said...

Fot the pruney bunch of regular kids, I will go with 101-150 please.

David said...

I think it is an easy puzzle (but I work with numbers). 1001 to 1050 please.

Anonymous said...

Wow, I thought this was tricky, in part because there are so many answers. I'm sure many people will come up with an answer that Will doesn't allow.

I suppose I'll request 401-450, please. I'm trying to skirt the line between correct and acceptable here. I suppose we'll see whether I'm right in a week.


Paul said...

51 - 100
Mi estación, su estación.
I speak very fluent Spanish.

Joe Kupe said...

Hi All, I broke one of the two cardinal rules of marathons. The first is drink often and never skip a stop. Nailed it. The second is don't go out too fast and no matter how fast you are going slow down. Well, that one stumped me as I lumbered in at 5:27;57 after completing the first half in 2:17! Relaxing my muscles now so will ponder a guess later this week. Thanks for all the well wishes.

Anonymous said...

Joe, congratulations on completing the marathon. I've completed many in my time, by which I mean that I've watched the end of the Olympic marathons on television.

By the way, did you happen to pass any grade-school classes on the way? And if so, could you see their eyes? Regular ones only.


Anonymous said...

I'll take 351 - 400. I'm no mathematician (Dammit, Jim, I'm an English Major, not a mathematician), but I have an answer that I think works well.

David said...

Congratulations. I have been running marathons for over 30 years and still go out too fast way to often. Learn from this one (way better than I ever did) and have a good next one.

legolambda said...

My odds of picking the right range are less than 50-50 if i choose 501-550. Still, that's what I'm going with.

Congrats on doing the thon, Joe Kupe.
Pretty respectable time, in my book.


Mendo Jim said...

I agree with David about this challenge's ease of solution.

If there is any constant in guessing the Range, it is that simplicity and complexity have little to do with it.

I'll go with 1300+.

I have to admit that Will did much better with alternative answers.

Alex B. said...

This question does not have a unique solution, but having the size limitation of a classroom does eliminate some possible answers. For instance, I don't think Will wants the solution of 137,904 students (of which 97,513 have blue eyes).

Paul said...

Alex B:

That would be highly irregular.

Anonymous said...

Alex B.:

Darn, that was my answer. (OK, not really. I originally stopped at four-digit answers--of which I found one--, but I agree that yours works.) I think I'll go instead with 4,684,660 (with 3,312,555 blue-eyed students) as my answer. As for the "regular" classroom, I'm going to assume it's an Internet classroom.

This problem's somewhat interesting, at least to me. It belongs to a class of mathematical problems that I won't identify today since that identification would serve as an impermissible hint. I think it's a safe bet that PM doesn't know about the broader issue, but then again, maybe he does.

I believe, by the way, that the answers for the class size must satisfy the requirement that sqr(2n^2-2n+1) (where n is the size of the class) has an interesting property. I can't imagine that that equation will help many though.


Henry BW said...

My usual 1051-1100, please.
I found one answer very quickly, and sent it in.
Microsoft Excel has found at least one more answer at a class size that I would consider credible: I predict that Will will go for a size that is not the one I chose. But at what date should we consider the class "regular"? Now, or when Martin Gardner was in grade school?

Ross Beresford said...

WYSO just got a $10 donation in honor of Zeke Creek's recent pick a range win. Congrats ZC.

Anonymous said...

Oh that clever Doctor Shortz! The key word of the puzzle is "regular," a condition achieved for the students with a little chocolate piece every morning.
Since there are no 'E's" or "A's" in Roman numerology, this leads to XLX, which is L minus X plus X or 50, which is the class size.
Of these 50 students 43.5 have blue eyes, 5.5 brown eyes and little Xerxes who has conjunctivitis (pink eye).
The math from there is elemental.
Thanks to the Puzzlemaster and Mr. Gardner for an interesting challenge.

B. Haven said...

I guess 301-350 for this week.

I think listeners avoid doing mental math. This didn't just pop into my head, but it's not too hard.

My dog has one blue eye and one brown, but people tell me you don't see that in people. I found a whole number of blue-eyed students.

zeke creek said...

Thanks Ross,
701-750, please.

Joe Kupe said...

151 - 200 please. Recovering nicely and should be back on the roads in a day or two! We went with our regular classroom answer, but also like our remote northern Michigan answer at the extreme other end of the range!