Sunday, November 6, 2011

NPR Puzzle 11/6/11 - Missing a Trick Somewhere

Here's this week's NPR Puzzle:
Take 15 coins. Arrange them in an equilateral triangle with one coin at the top, two coins touching below, three coins below that, then four, then five. Remove the three coins at the corners so you're left with 12 coins. Using the centers of the 12 coins as points, how many equilateral triangles can you find by joining points with lines?
I have an answer. Is it the right answer? Probably not. I figure there's a trick and I'm just not seeing it.

Your answer is almost certainly correct. Send it in to NPR here.

Photos of equilateral triangles:







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.  The winner gets a puzzle book of our unspecified choosing.
490 people. (I'm loving the Unpaid and Underappreciated Intern.) *mwah* Alas, no one won. As you didn't win last week, try to win this week. Pick a range in the comments to see if you'll win a prize!

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, 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").  And yes, this rule is most-likely obsolete but I just like having fine print. 

9 comments:

David said...

I have an answer, but I'm not quite ready to send it in. I came up with an answer without using pencil and paper (p&p) by thinking of how many eqilateral triangles there were using all 15 points, then subtracting those formed with the three extreme points. I came up with a higher answer when using p&p.

If I used the same method of starting with all 15 points and then subtracting, I came up with the same number to subtract from the total both with and without p&p. That is, the triangles I missed did not use any extreme point.

For a supplemental puzzle (one we probably should not answer until Thursday), how many equilateral triangles using all 15 points?

I'll go with my standard 1001 to 1050 range.

Anonymous said...

Is there any systematic way of determining whether you have the correct answer? I suspect not, so the number of answers will be a lot higher than the number of correct answers, and I assume the poor intern will not distinguish.

My usual 501-550, please, but I'm sure that is too high.

Henry BW

skydiveboy said...

I will go with 300 and hope they only count correct answers, and even then I will most likely be on the high side.

David said...

I am now comfortable with my answer and have determined a general way to calculate the number of equilateral triangles, both and without the extreme points, starting with any size equilateral triangle. I'll see if I can figure out a simple explanation for Thursday.

Marie said...

I'm hoping people are more interested in geometric than word puzzles. I'll take 701-750, probably too high, oh well.

Mendo Jim said...

I used to enjoy this kind of puzzle when I was a kid.

Joe Kupe said...

My friends and I have answers just a few apart from each other. We'll wait until later tomorrow to confirm and then post to NPR. In the meanwhile I'll go with 351 - 400.
Joe Kupe

Paul said...

601 - 650, please.

Curtis said...

New to this blog. I'll take 151 - 200.