Blogs tend to be lonely pursuits; at least most of the ones I read– they focus on narrow interests (gaming, history, math, physics, astronomy), there really isn’t a lot of repartee between the primary author and his audience. Many of them become declarative in tone after a while. As for this blog, I know people visit it, but I’m never certain people read anything or engage in a post beyond the surface skim mode perfected by the Internet age. I’m sure more interaction on 3PoS would be fun, but what would I do to create that? Post a series of video reviews? Get in the game review business? Start a REAL regular podcast on something people are interested in? Nah, I don’t think so. I don’t have the time to be another Tom Vasel. Besides, there’s Tom Vasel already, and he’s doing a great job. Still, it’s nice to discover that every once in a while, someone reads and engages with something that gets posted here, and such was the case today. The recent number grid concentration puzzler was posted with the usual lack of fanfare and pessimism by your humble narrator on 09 December. I posted the answer in a spreadsheet form (the same one that created the puzzle, by the by) on 21 December. Perhaps I should have waited a week or so more, because today I received a very nice email from Mr. Jonathan Franklin, who hails (I think) from the West Seattle area. Read on after the break.
Proof that our group both read your post and worked the problem.
———- Forwarded message ———-
From: Robb Effinger (email withheld)
Date: Fri, Dec 9, 2011 at 10:17 PM
Subject: Re: Puzzler: Number Grid Concentration
Basically trial and error, with excel displaying the difference to make things pretty painless. I used the average missing amount to start things off, and there are some tricks you can do to move the incorrect values around to the row/column you want them in. It actually looks like there are at least 9 correct solutions – you can mess with (82, 96), (82,99), (107,96), and (107,99).
On Fri, Dec 9, 2011 at 4:49 PM, Nathan Beeler <email withheld> wrote:
I was thinking you could do it with a crap ton of simultaneous
equations, but that seemed like more work than fun. I also looked at
treating it like a painting puzzle, and trying to constrain numbers
that way. But only got so far in a few minutes and had to get back to
working. Curious to hear what Senior Robb did.
On Fri, Dec 9, 2011 at 1:46 PM, Mark Engelberg <email withheld> wrote:
> I’ll take your word for it :). Did you use any particularly clever
> strategy other than trial and error?
> On Fri, Dec 9, 2011 at 12:20 PM, Robb Effinger <email withheld> wrote:
>> I think you messed up the analysis, because I think this grid works 🙂
>> 16 17 12 7 12 10 10 15
>> 3 18 19 16 20 6 14 6
>> 2 9 13 11 10 11 2 14
>> 17 6 6 16 18 16 6 11
>> 16 8 15 3 15 15 6 3
>> 6 18 14 11 20 20 4 20
>> 20 5 17 14 13 11 13 5
>> 8 1 11 1 3 12 20 11
>> On Fri, Dec 9, 2011 at 1:08 PM, Mark Engelberg <email withheld>
>>> I don’t think it’s possible. How sure are you that it is solvable?
>>> Here’s my line of thinking:
>>> Imagine putting even numbers in all the empty spaces except the spaces
>>> with the following coordinates, which would be odd:
>>> (79,113) (79,96)
>>> (111,96) (111,72)
>>> (75,98) (75,96)
>>> At this point, all the sums have the correct parity except row 81.
>>> I don’t see any way to fix the parity of row 81 without destroying the the
>>> parity of other things.
>>> Did I mess up this analysis?
So the long and short of it is that the “West Seattle Gaming Group” not only read the post, but they took the time to digest it and try to solve the problem. What can I say, except that I am touched? Thanks for trying it, gentlemen. And thank you for taking the time to reply back. I should have let you stew on this one for another week before providing the answer so quickly.
Original Post: misternizz.wordpress.com/2011/12/09/puzzler-number-grid-concentration/
Solution (on the same spreadsheet that created this puzzle): https://misternizz.wordpress.com/2011/12/21/bookkeeping-answers-to-09-dec-puzzler/
West Seattle Gamers’ Yahoogroup: http://games.groups.yahoo.com/group/wsgamers/