Sunday, October 7, 2012

NPR Puzzle 10/7/12 - Will Shortz is Triangulating Again!

Here's this week's NPR Puzzle:
Draw a regular hexagon, and connect every pair of vertices except one. The pair you don't connect are not on opposite sides of the hexagon, but along a shorter diagonal. How many triangles of any size are in this figure?
Don't have an answer for you, but here's what we think the figure should look like:

I'll do a quilt-y analysis of the number of triangles for Thursday's blog post. In the meantime, go ahead, print this out, use some colored pencils and then send the correct answer in to NPR using their regrettably rectangular contact form here.

By the way, here's where the World Puzzle Championships are taking place: Kraljevica, Croatia. And here's a picture from Flickr:


Time for pictures of triangles! (If these aren't enough, look here and here for even more triangle photos.)

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 puzzle book of our choosing.
We got REAL numbers this week: 140 entries, of which 55 had the intended PROSE/POEMS answer. Alas, none of us guessed that low. So back to the drawing board (see above) and send in your favorite range and see if you can win.
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."), AND two separate people picked the ranges of numbers just before and just after that round number, the prize will be awarded to whichever entrant had not already won a prize, or 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 July 2012, this rule is officially no longer obsolete (and also I just like having fine print). 


Curtis said...

I'm going say that many folks will submit the wrong answer. I'll go with 351-400 again.

skydiveboy said...


Anonymous said...

I cannot find any analytical solution. My two attempts at enumeration gave answers so different that I threw the paper into the recycling bag and went to do something different.

As for last week, several of you had been complaining that recent weekly puzzles were too easy, but a puzzle where apparently more than half the entrants had the same wrong answer is presumptively flawed.

My usual 1051-1100, please, on the assumption that the announced figure will be for total entries, not correct entries.

Henry BW

EKW said...

Dear Henry,

I think there is analytic help if you look at the problem with all the diagonals included, and then see what goes away when you remove one. But this is definitely a non-trivial
counting problem.


Based on last weeks fiasco I think
I will try fewer than 50 correct answers this week!

Mendo Jim said...

Even the Puzzlemaster's diehard apologists are scratching their heads at his re-definition of "anagram."
Has anyone in history gotten more milage out of the genre?

If dreary/dreamy was to be disallowed, it should have been based on the weakness of the antonym. Prose/poems was shaky enough in that regard.

Gotta admit he's got the brass ones to throw out 85 answers and admit 55.
He majored in enigmatology with perhaps a minor in arrogance.

Here is where I always hope I am wrong: Don't look for Will to clear this up.
The most likely change will be to make sure the correct/total ratio is not divulged again.

I'll pass on the triangle counting, thanks.

David said...

In this past Sunday's NYT crossword puzzle, one clue was "Did ordinary writing" and the answer was "prosed". The opposite must be "poemed".

This week is not a puzzle for during a run, but I think I can count.

I'll go with my favorite range, 1001 to 1050.

Anonymous said...

Dear EKW, yes, that was one of the two methods I tried. Henry BW.

EKW said...

Dear Henry,

What was the other method?


Curtis said...

Dear Henry and and EKW,

¿Why the formalities with your comments?


Sincerely and with warmest regards,

EKW said...


Just trying to be polite, and not familiar with the standard format.

Curtis said...


I hope you took my comment in the good-natured sense that I meant it.

EKW said...

Curtis, yes, I think I did.

I also thought I had submitted the correct answer to the puzzle, but I was wrong. I have a short discussion of the correct answer, with references, which I will post tomorrow afternoon.

KDW said...

I am unsure whether we are guessing the total number of entries or only the number of correct entries. Either way, may I please have 201-250?

Marie said...

Okay, I've counted forwards and backwards and feel confident in my solution. However, I felt confident about dreary/dreamy too. I will submit my solution and whine a little about Will's cavalier dismissal of my last effort. 801, please.