Thursday, June 16, 2011

NPR Puzzle 6/19/11 - Wearing Many Hats

Here's this week's NPR puzzle:
A hat room contains a wall with 49 pegs, arranged in a 7-by-7 square. The hat clerk has 20 hats that are to be hung on 20 different pegs. How many lines, containing four hats in a straight line, is it possible to produce? A line can go in any direction: horizontally, vertically or obliquely. To explain your answer, number the pegs in order, from 1 in the upper left corner to 49 in the lower right corner; list which pegs you put the 20 hats on, and give the total number of lines containing four hats in a row.
I got Ross to make a snazzy graphic:


We make that 18 lines.  Did anyone get more?  Note that only four lines are orthogonal (vertical or horizontal); the rest are "oblique" just as Dr. Shortz said.

Here's the number sequence: 1, 4, 7, 10, 12, 16, 17, 19, 20, 22, 28, 30, 31, 33, 34, 38, 40, 43, 46, 49

All credit to Ross on this -- I'm not particularly good at these sorts of puzzles, which is interesting because I do enjoy the mathematical puzzles published four times a year in the London Times in The Listener series.  I just don't have the software compiler's efficient use of logic for this sort of thing.  Well done, Ross.

And if skydiveboy would like to show us a way to get more lines, I'll edit this post to include his version.

More hat photos!  (They're never-ending sources of fun, even if I wouldn't be caught dead in one!)





Time for  ...
P I C K   A   R A N G E

Here are this week's picks:
Fewer than 50 -- Mendo Jim     
50 - 100
100 - 150 -- Ross
150 - 200 -- Dave
200 - 250 -- David
250 - 300
300 - 350 -- Marie
350 - 400
400 - 450
450 - 500 -- Magdalen
500 - 550
550 - 600
600 - 650
650 - 700
700 - 750
750 - 800
800 - 850
850 - 900
900 - 950
950 - 1,000
1,000 - 1,050
1,050 - 1,100
1,100 - 1,150
1,150 - 1,200
1,200 - 1,250
1,250 - 1,300
1,300 - 1,350
1,350 - 1,400
1,400 - 1,450
1,450 - 1,500

1,500 - 1,550
1,550 - 1,600
1,600 - 1,650
1,650 - 1,700
1,700 - 1,750
1,750 - 1,800
1,800 - 1,850
1,850 - 1,900
1,900 - 1,950
1,950 - 2,000
2,000 - 2,050
2,050 - 2,100
2,100 - 2,150
2,150 - 2,200
2,200 - 2,250
2,250 - 2,300
2,300 - 2,350
2,350 - 2,400
2,400 - 2,450
2,450 - 2,500

2,500 - 2,750
2,750 - 3,000
3,000 - 3,250
3,250 - 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")

8 comments:

Paul said...

Adding together the numbers in Ross's sequence yields 500; the same as the number of miles traversed last Sunday by racers on the "tricky triangle".

My Hat It Has Three Corners.

woozy said...

Very good. I should have gotten that but I didn't.

My hat may or may not have three corners; I don't know because my hat is indescribable.

Paul said...

woozy,
Are you sure it's your hat that's indescribable, or could it be your haberdasher?

woozy said...

I got the hat from an ancester of mine who was rather reknowned for having an indescribable hat. Although to be honest, there was one gloomy morning around page 86 or so where everything appeared drabber and my ancester's hat appeared merely describable. But things got better.

Mendo Jim said...

I think you are making that up.

Paul said...

I think "ancestor" is the more recognized spelling of a synonym for "forebear".

I think "haberdasher" may have meant essentially the same thing as "hatter" in some place, and at some time; but that this is neither that place nor that time.

I think we're all making it all up.

woozy said...

Mondo Jim, it is not I who am making it up. I am just a mere device for others.

Oh, and in the big match tomorrow between the Lucky Charms and the Bagel Schmears, well I'm big in the charm department. Goooo Lucks!!!

Paul, despite being rather good at crosswords and puzzles, I'm a rather careless speller and typist. Yes, ancestor is the correct spelling for the synonym for forebear. Although, I am actualy more of a fourbear myself, being square and cuddly and all.

woozy said...

Holy Crap! Slap me sideways back to Wednesday for not getting my own reference from Mondo Jim.

Very good, sir. "The Golux makes things up." *VERY* good, indeed!