Sunday, December 5, 2010

NPR Puzzle 12/5/10 - I Saw So -- Lee's Triangles

This week's puzzle:
Draw a 4x4 square. Divide it into 16 individual boxes. Next, draw a diagonal line from the middle of each side of the square to the middle of the adjoining side, forming a diamond. And, finally draw a long diagonal line from each corner of the square to the opposite corner, forming an X.
How many triangles can you find in this figure?
Note that the online version was WRONG.  This is the correct version.  The short answer is that we don't know, but I feel comfortable reminding you to count all the big triangles as well as the little ones.  But you already thought of that.  We'll have a number for you on Thursday.  We don't claim that it will be the right number...

Submit your answer to NPR here.  And PLEASE don't give too much away in the comments.

Many thanks to Mendo Jim for suggesting that an accurate -- but unlikely to be correct -- answer is "All of them."

We are away from home until Sunday afternoon, so I'll amend this post then to announce the winner (if there is one) of the Pick-A-Range contest.  But in the meantime go ahead and vote on how many answers this geometric puzzle will get this week.  Alas, no one picked 900-1,000, so no winner.

Here are some triangulated photos:

Time for ...

P I C K   A   R A N G E

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.  Ross and I guess last, just before we publish the Thursday post.  After the Thursday post is up, the entries are closed.

[As always, troublemakers risk winning the American Girl puzzle book, so play nice.  :-)]

Here are the ranges:

Fewer than 100
100 - 200
200 - 300
300 - 400
400 - 500

500 - 600
600 - 700
700 - 800
800 - 900
900 - 1,000

1,000 - 1,100
1,100 - 1,200
1,200 - 1,300
1,300 - 1,400
1,400 - 1,500

1,500 - 1,600
1,600 - 1,700
1,700 - 1,800
1,800 - 1,900
1,900 - 2,000

2,000 - 2,100
2,100 - 2,200
2,200 - 2,300
2,300 - 2,400
2,400 - 2,500

2,500 - 3,000

3,000 - 3,500

3,500 - 4,000

4,000 - 4,500

4,500 - 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, AND two separate people picked the ranges leading up to and leading up from 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")


Jimel said...

The online version is different than the audio version. On air Will says to divide the 4x4 square into SIXTEEN boxes.

Jimel said...

Picking a range depends on whether they correct the online version of the puzzle. I think I'll assume they don't get around to it for awhile and go low choosing the 300-400 range.

Jimel said...

I note that by 1 PM EST NPR has corrected the online version of the puzzle.

Magdalen said...

Okay, I've fixed it. Too bad -- I had an answer to my original version! Back to the drawing board...

Jimel said...

I did the bogus one last night -- I clicked on my NPR bookmark to check on something else and saw that the new puzzle was already up. I guess it was after midnight. You can imagine my surprise as I was lying abed listening and heard Will say "sixteen." Of course 16 is a lot easier to draw than 6 and gives you a dizzying number of triangles.

DAPF said...

Can I get my usual range: 700-800 please?

I wonder if Will is running out of good word puzzles. But I would find this surprising, since I sent him one or two GREAT ones (of course) that never made it to the air... 8^)

henry.blancowhite said...

The question actually asked is "How many triangles can you find?" and not "How many triangles are there?", so any good-faith answer should be accepted as correct.

Mendo Jim said...

Henry is right, of course, realizing that sort of a low-impact answer is really called for. Unfortunately this requires nuance and subtlety, never the Pzmasters strongpoints.
As for the challenge itself, there may be actual danger here as triangles seem to be multiplying without end. Every time I think I have them all, others (usually in fours, for some reason) pop up.
Right now I have as many of them as I was going to ask for a Range, so I'll hold off until the fecund little devils stop breeding.
I guess we discovered the shortcomings of getting a headstart. At least working on 6 instead of 16 gave a little practice.

Dave said...

Nice answer, Henry. I haven't taken the time to work this out yet, but I'll take the coveted 500-600 slot.

David said...

I'll go with 1500 to 1600 entries.

I tried to do the puzzle twice and came up with the same answer both times, bu I'm still not positive I'm right.

Anonymous said...

Is contest for the number of entries or the number of correct answers? I will say 200-300 which ever.

Magdalen said...

Anonymous -- Could you provide a name or identifier in your comment, so we don't accidentally award a prize to the wrong "Anonymous"?


Mendo Jim said...

What a great book title! "The Wrong Anonymous, a Case of Mistaken Identity."
Well, this one presents a problem for picking a Range.
If Henry is right, then anyone sending in however many they found is a winner.
If only the correct total is accepted, there are likely to be just a few.
And there may not even be agreement on the right number.
There is a nice confluence, however, of total triangles and the Range I want: Fewer than 100.
I guess tomorrow is the time to share our answers.

Anonymous said...

I am the right anonymous with the 200-300 answer.

Fell free to call me Grace

David said...

The Wednesday Puzzler:
Rearrange the letters in “Anonymous” and “Grace” to get how you might be able to buy rodent-flavored wet cat food at Costco (3 word phrase, 1/10/3), if an alternate spelling of a made up word is allowed. (Scroll down for answer.)

Answer: “A GYNORMOUSE CAN”. Sorry, it’s been a long day.

Magdalen said...

LOL! And welcome, Grace.

Magdalen said...

Mendo Jim -- the real question is whether they'll announce the number of CORRECT entries, or just the number of entries.

If it's the former, then you may well be right (fewer than 100), but if it's the latter, it could be higher than we all expect.

David said...

It seems to me in the past that sometimes they have announced correct entrants and sometimes total entrants. Maybe it depends on how busy the intern is.