Thursday, November 10, 2011

NPR Puzzle 11/6/11 - Hazard Warnings are Triangles!

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 it on good authority (Henry) that the number is 25.

Here's how Henry got his answer, which isn't my answer but then I said I'd get it wrong

Number the points

 - - - - 1 - - - -
 - - - 2 - 3 - - -
 - - 4 - 5 - 6 - -
 - 7 - 8 - 9 -10 -
11 -12 -13 -14 -15
(I think I got the padding right, so that will work if you cut and paste it into Courier.)
Remove nos 1, 11, 15.
13 single-length triangles.
4 double-length triangles 2-7-9, 3-8-10, 5-12-13, 4-6-13.
6 sideways triangles 3-4-9, 5-7-13, 6-8-14, 2-6-8, 4-9-12, 5-10-13
2 skewed triangles 2-10-12, 3-7-14. 

More photos of equilateral triangles:








Time for ...
P I C K   A   R A N G E
Here are this week's picks:
Fewer than 50
 51 - 100
101 - 150
151 - 200
201 - 250 -- Ross
251 - 300 -- skydiveboy
301 - 350 -- Magdalen
351 - 400 -- Joe
401 - 450
451 - 500
 
501 - 550 -- Henry
551 - 600
601 - 650 -- Paul
651 - 700
701 - 750 -- Marie
751 - 800
801 - 850
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 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")

2 comments:

Natasha said...

Did you mean 5-12-14 instead of 5-12-13?

Anonymous said...

Yes.