Thursday, October 11, 2012

NPR Puzzle 10/7/12 - My Triangle Quilt!

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?
We make the answer to be 82, and here they are, in ready-to-stitch quilt format:


The stunning thing is, leaving out that one line reduces the total from 110 triangles to 82. You wouldn't think a single vector would have that effect.

(The relevant proof for a completed hexagon is here. Here's the key sentence:
The number of triangles is 1, 8, 35, 110, 287, 632, 1302, 2400, 4257, 6956 for polygons with 3 through 12 sides.
I've highlighted the sides=6 number in red.)

I would like to thank Crossword Man for his meticulous work double-checking my work...and finding the four triangles I couldn't see.

Here are some prettier quilts for you to admire. I didn't make any of them. Okay, I made one of them. (Try & guess which...)






Time for
Just to reiterate, we are looking for the number of entries. If the announcement includes the number of correct answers, that's a bonus datum.

Here are this week's picks:

Fewer than 50 -- EKW
 51 - 100 -- Ross
101 - 150
151 - 200 -- Magdalen
201 - 250 -- KDW
251 - 300
301 - 350 -- skydiveboy
351 - 400 -- Curtis
401 - 450
451 - 500
 
501 - 550
551 - 600
601 - 650
651 - 700
701 - 750
751 - 800
801 - 850 -- Marie
851 - 900
901 - 950
951 - 1,000
1,001 - 1,050 -- David
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 + 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 still just like having fine print). 

2 comments:

Liz Gorski said...

Beautiful quilting, Magdalen! What a glorious blend of art and science. I love it!

Paul said...

I'll guess quilt #1 is Magdalen's work.