NPR Puzzle - 1/6/13 -- Sweet Sixteen

How did you all get on with last Sunday'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?

This was originally a Sam Loyd puzzle from 1913. I suspected that the original might be found somewhere on the interwebs, and indeed located it in this Cyclopedia of 5000 Puzzle Tricks and Conundrums. I know from the comments that at least one reader did alike.

Will went to some length to change the puzzle around, removing all mention of cabbages and inverting the sense of the puzzle, so it involved adding 10 markers to an empty grid, rather than removing 6 from a full grid. Here then is the original wording:

Mrs. Wiggs is explaining to King Puzzle-pate that there are fourteen even rows of cabbages [in a full grid] according to magic square rules. She asks him to take away six cabbages and leave sixteen rows with an even number in each; ...

So the maximum number of even-row lines is 16, and here is one of the arrangements that achieves it:

You might be thinking "what happened to the cabbage, that Prince of Vegetables, the only veggie you can play on the piano?" The following is for you:

Everyone's Fav Veggie

Cabbage Patch Doll

Oh no, not another cat in a box

Cabbages and Condoms

If you work out how this involves cabbage, do tell in the comments

Time for

Here are this week's picks:

Fewer than 50 -- skydiveboy  51 - 100 -- KDW 101 - 150 -- Mendo Jim 151 - 200 -- Paul 201 - 250 -- jan 251 - 300 -- Joe Kupe 301 - 350 -- zeke creek 351 - 400 -- Curtis 401 - 450 -- Marie 451 - 500 -- EKW   501 - 550 -- Magdalen 551 - 600 601 - 650 -- Ross 651 - 700 701 - 750 751 - 800 801 - 850 851 - 900 901 - 950 -- Margaret 951 - 1,000

1,001 - 1,050 -- David 1,051 - 1,100 -- Henry BW 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  > 5,000  > 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).