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original photo from Richard Masoner Edited by Brian Not sure what got me thinking about this today, but I was musing about the commutative property, and how it applies to addition and multiplication. (Yeah, it was a pretty boring morning.) Specifically, I was thinking about the word, “augend”. The augend of an addition problem is the [...] Q: When is a Compromise not a Compromise? We talked about “red herrings” in the previous posts about “The Case of the Missing Dollar.” I occasionally do after-school presentations of MathMagic for the C.R.O.P. program in rural upstate New York. I’ve been participating in the program for years, as a local artist (magician). The program pays a very small honorarium, and a travel budget (Monday I drove 120 miles round-trip for peanuts) Most of the artists do it out of love of bringing their art to children who otherwise may never get exposed to it. It is a labor of love to all concerned, but it is a great mission. The Creating Rural Opportunities Partnership (CROP) After School and Summer Program is a program which does just what it is named. In it’s mission statement:
Over the last few years, funding for this excellent program has dwindled. Sound familiar? Art and after-school programs are typically among the first to get their throats cut when the government feels it needs to cut costs.
Original Photo by Norsehorse Edited by Brian Ah, I love it when readers beat me to the punch! The comments to the original post pretty much sum up the paradox and it’s solution very well. Khaled’s and Mark’s comments illustrate perfectly one of the things I wanted to point out about this puzzle. That point is: Just because something is phrased a certain way is not reason to assume that that phrasing is the best way to represent the problem. And one way to critically examine the situation is to reframe it in a mathematical equation. Khaled said, “Interesting how, once you assume that you can implicitly trust a given source, you can be led through any logic, or illogic, and have a lot of trouble pulling yourself back to a critical mindset.” How true. Then Mark gave a good method to understand how to see where the paradox lies when he said, “I started to write an equation, because properly written equations can solve all counting problems, but then realized that this was pointless, because adding 2 dollars to the 27 dollars the guests paid did not reflect what happened.” Exactly! The question was phrased to lead you to believe that because the facts were a certain way (which it accurately represented) you had to see it in a certain way (which was anything but accurate). Continue reading Math Puzzle – Case of the Missing Dollar(?) Part 2 (The Flip Side) →
Original Photo by Norsehorse Edited by Brian There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this: Three men go into a motel. The man behind the desk said that [...] I found this on a weird little personal blog: Why has math been hated by some? Because it requires them to think and forces them to give the correct and exact value. Math has a clear distinction of right and wrong. Most people love to speak about any issue, but hate to accept that they’re wrong. That’s the [...] Are you a homeschool parent struggling to teach your child math? Or are you just frustrated by the way your kid’s school teaches math? You’re definitely not alone, and you’re in great company. Here is part of a story from a father who faced the same thing. It’s a comment left by Mark, a reader at [...] (Or “The Seamus on Mitt Romney”)
Sometimes you read a story that just grabs you. I got one forwarded to me today that, at first glance, seems to have nothing to do with math. But since Math Mojo readers know that math is more meaningful than that stuff they shoved down your throat in school, I think you’ll appreciate this one. Bear with me. In the summer of 1983, Mitt Romney took a vacation with his wife and five sons, to his parents’ cottage on the Canadian side of Lake Huron. The trip from Boston was twelve hours long. According to an article in the Boston Globe by Neil Swidey and Stephanie Ebbert, Globe Staff, June 27, 2007:
“… As the oldest son, Tagg Romney commandeered the way-back of the wagon, keeping his eyes fixed out the rear window, where he glimpsed the first sign of trouble. ”Dad!” he yelled. ”Gross!” A brown liquid was dripping down the back window, payback from an Irish setter who’d been riding on the roof in the wind for hours. “As the rest of the boys joined in the howls of disgust, Romney coolly pulled off the highway and into a service station. There, he borrowed a hose, washed down Seamus and the car, then hopped back onto the highway. It was a tiny preview of a trait he would grow famous for in business: emotion-free crisis management.” Yeah, otherwise known as “compassionate conservatism.” You know that to “conserve” means “to not use,” or “to use as little as possible.” To conserve your compassion for what? Your cronies? Your sons, who you conserve for your political agenda, but not to fight in a war that you support? Certainly not for your dog… |
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