A funny thing happened . . . on the way to this entry. Actually a couple of them. Let’s try to deal with both of them . . .
Event 1: Previously, I mentioned – in a footnote – a problem called the “Calendar Cube” problem. Interestingly, the footnote made it into the digital version of the newspaper column (and into these blogs, of course), but not into the more crowded printed version of the newspaper.
I only discovered this myself when I began to receive solutions to the problem, along with other questions as to where the problem went. So let’s deal with that loose end first.
The problem statement, roughly: Arrange the digits 0 – 9 on two blank wooden cubes in order to be able to represent each date in any given month. I suspect you’ve seen such calendars in banks, etc. It’s a fun challenge, partly because there’s a subtle ‘trap’ or two lying in wait. I won’t share ‘the answer’ here and now (part of the point of that previous column, after all, was the 8th grader who wanted to solve it herself!).
My favorite newspaper response came from Dan Felshin of Springfield, proudly claiming to be 81 and a lover of all things needing logical approaches. I’ll share more of Dan’s (and wife’s) response, and also discuss the problem more, next time around.
Event 2: Did you see David Hough’s column(s) in the News-Leader back on Jan 13th (& 20th)? (If not, you may read it here: Hough.) He spoke of the discovery of old slate boards full of ‘good stuff’ hidden behind some blackboards in an Oklahoma City classroom.
Among the other fascinating things found there – it must have been a huge slate board – David describes the following ‘mystery’:
Around the perimeter of a red chalk circle are written the following orange-yellow numbers: 8, 7, 4, 12, 7, 11, 9, 8, 6, 4, 2, 3 ,5, 7, 9, 3, 6, 8, 7, 5, 6, 3. In the center of the circle is 2X, 3X, 4X, 5X, 6X, 7X, 8X.
He moves on to other descriptions, and seems to leave this as a puzzle for us to wonder about. Loving these kinds of mysteries, I’d like to share my own conjecture.
I’m convinced this area of the board was a set-up for a drill or game involving good old ‘times tables’. My guess is that students chose (or were assigned) a number in the center, like 6X, and then, using the numbers around the outside, had to say as many of the 6-times tables as possible.
Two of the biggest clues for this conjecture – at least for me – deal with the numbers that are – and aren’t – in or around the circle. In the first place the numbers around the circle include 11 & 12, but no higher. This coincides with the typical range of times tables (at least in my day!). Second, there is NO ‘1’ or ‘10’, either inside or outside the circle. That’s probably because products involving 1 or 10 don’t need to be memorized. I have my own theories as to why there is no 9X, 11X, or 12X.
This could all be ‘wrong’ of course – who knows what actually occurred? Any thoughts? – is this a crazy guess? On the other hand, it’s fun to at least puzzle over a conjecture, isn’t it? What’s your conjecture?
And besides – these kinds of things are supposed to keep one’s mind young – it seems to have worked for Dan Felshin – maybe it’ll work for me!
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