Sunday, April 18, 2010

Suck it Will Shortz

On Thursday, I posed to the tiny bowling world which peruses this blog a problem that I thought might lie dormant for some time. Yet, upon returning from slaying some rainbow trout this afternoon at North Crow Reservoir, I found an email awaiting me from Garrett Boni of Baton Rouge, Louisiana. Garrett has proven to me that he also deserves the title of "Puzzle Master," which prior to this moment had been reserved for Will Shortz.

The problem I posed concerned the 3-9 "sleeper" leave. In essence, I asked what is the margin of error in picking up this shot if you attempt to collect the spare by driving the front pin into the back. I set it up as a problem in geometry. According to Mr. Boni, he was able to complete the solution in about 1 and 1/2 hours. Up to this point, I had not attempted a solution myself. Thanks to Garrett, I found myself in the position of having to do trigonometry on a Sunday afternoon, a misdemeanor in Wyoming. Here is Garrett's work:
Garrett used an elegant geometric solution; click on that image above if you are interested in the details. In short, he found that you could miss the center of the pin by up to 0.5496 inches to the right and still pick up the spare. In theory, you could also miss by that amount to the left. So, according to his calculation to pick up the 3-9 by driving the front pin into the back, you have to place the ball within an area approximately 1.1" in width.

I should note that if one measures the margin of error perpendicular to the long axis of the lane, it is reduced to 0.546", a difference of less than 1%. So Garrett, congratulations. In addition to having earned the much coveted title "Puzzle Master", you have also won a free subscription to the BM Report.

[And congrats to HCLC Doc, who arrived at the same solution independently.]

UPDATE: Upon further review, I wonder if we are missing part of the solution here. I think we have solved for how much margin of error there is in striking the pin, but this is not necessarily the same thing as the margin of error for the shot. In other words, I think it is possible to still pick up the spare if the center of the ball misses the center of the pin by more than 0.6". The factor left out of these solutions is the curvature of the ball.

4 comments:

  1. That other dude's chart caused me to reboot.

    This is why I just hope to hit the three-pin head on. (And this is why Captain Kirk would beat Mr.Spock at bowling.)

    AND another thing. The team doctor is always telling me not to think. I THINK, therefeore, thathe doesn't practice what he preaches.

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  2. It made me grin from ear to ear. Except for you, Doc, kafka, and MD, I often feel like I am writing to the void. Then, I get this marvelous chart in my email of nowhere. Such things not only continue to chip away at my deep seated stereotypes about bowlers, also but make me a feel akin to some random guy I have never met in Louisiana. Good stuff.

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  3. Yeah, I know what you mean. Some anonymouse poster said he copied the SUCK emblem from my blog and made a wallpaper (?) out of it...

    The stats I get every week on my blog reveals that there are LOT of lurkers out there, man.

    You've got to keep posting to this blog over the summer or Mick will need therapy.

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  4. Interesting. I will assume that's digital wallpaper. I'll post now and then in the summer.

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