I was hit by a massive computer malfunction this week, the kind that forced me to buy a new computer and spend half a week copying stuff over from a limping hard drive and hoping it would maybe work if I held things just right. Mercifully, Comic Strip Master Command gave me a relatively easy week. No huge rush of mathematically-themed comic strips and none that are going to take a thousand words of writing to describe. Let’s go.
Sam Hepburn’s Questionable Quotebook for the 14th includes this week’s anthropomorphic geometry sketch underneath its big text block.
Eric the Circle for the 15th, this one by “Claire the Square”, is the rare Eric the Circle to show off properties of circles. So maybe that’s the second anthropomorphic geometry sketch for the week. If the week hadn’t been dominated by my computer woes that might have formed the title for this edition.
Werner Wejp-Olsen’s Inspector Danger’s Crime Quiz for the 15th puts a mathematician in mortal peril and leaves him there to die. As is traditional for this sort of puzzle the mathematician left a dying clue. (Mathematicians were similarly kind to their investigators on the 4th of July, 2016 and the 9th of July, 2012. I was expecting the answer to be someone with a four-letter and an eight-letter name, none of which anybody here had. Doesn’t matter. It’ll never stand up in court.
John Graziano’s Ripley’s Believe It Or Not for the 17th features one of those astounding claims that grows out of number theory. Graziano asserts that there are an astounding 50,613,244,155,051,856 ways to score exactly 100 points in (ten-pin) bowling. I won’t deny that this seems high to me. But partitioning a number — that is, taking a (positive) whole number and writing down the different ways one can add up (positive) whole numbers to get that sum — often turns up a lot of possibilities. That there should be many ways to get a score of 100 by adding between ten and twenty numbers that could be between zero and ten each, plus the possibility of adding pairs of the numbers (for spares) or trios of numbers (for strikes) makes this less astonishing.
Wikipedia led me to this page, from Balmoral Software, about all the different ways there are to score different numbers. The most surprising thing it reveals to me is that 100 isn’t even the score with the greatest number of possible scores. 77 is. There are 172,542,309,343,731,946 ways to score exactly 77 points. I agree this ought to make me feel better about my game. It doesn’t. It turns out there are, altogether, something like 5,726,805,883,325,784,576 possible different outcomes for a bowling game. And how we can tell that, given there’s no practical way to go and list all of them, is described at the end of the page.
The technique is called “divide and conquer”. There’s no way to list all the outcomes of ten frames of bowling, but there’s certainly a way to list all the outcomes of one. Or two. Or three. So, work out how many possible scores there would be in few enough frames you can handle that. Then combine these shortened games into one that’s the full ten frames. There’s some trouble in matching up the ends of the short games. A spare or a strike in the last frame of a shortened game means one has to account for the first or first two frames of the next one. But this is still an easier problem than the one we started with.
Bill Amend’s FoxTrot Classics for the 18th (rerun from the 25th of May, 2006) is your standard percentages and infinities joke. Really would have expected Paige’s mother to be wise to this game by now, but this sort of thing happens.