NPR Puzzle - 1/6/13 -- Little Boxes

Good morning puzzle people ... it's Crossword Man again with the NPR Sunday Puzzle commentary. Today's graphical puzzle is from the inimitable Sam Loyd and was first published exactly 100 years ago in 1913.

What other puzzle was first published in 1913? Why, the crossword. Yes, 2013 is The Centenary Of The Crossword, although the exact anniversary is on December 21 ... the first word cross [sic] puzzle was conceived as just another piece of holiday fun. And they thought it couldn't last.

Anyway, here's the gist of this week's NPR puzzle:

Draw a square that is four boxes by four boxes per side, containing altogether 16 small boxes. There are 10 ways to have four boxes in a line — four horizontal rows, four vertical columns, plus the two long diagonals. There are also eight other shorter diagonals of two or three squares each. The object is to place markers in 10 of the boxes so that as many of the lines as possible have either two or four markers. What is the maximum number of lines that can have either two or four markers, and how do you do it?

Here is my artist's impression of the setup:

How do you fill those little boxes, and more to the point how do you convey that using the submit your answer link? At least you get 64,000 characters to express yourself.

Here are some completely random things to get you thinking inside the box:

Time for

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. Or skip the comments and send an email with your pick to Magdalen (at) Crosswordman (dot) com. 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 choosing.

There were around 650 entries for last week's puzzle, and we all picked too high ... though I got closest and hereby claim the prize.

You can win either a puzzle book or the warm glow of satisfaction knowing you're a generous person who caused a contribution to the Fairfield County Community Foundation. Guess the range for this week's puzzle, and good luck!

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 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 just like having fine print).