Sunday, May 24, 2015

470: Poor Alex Bellos

Normally, I'm glad when the nedia talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.

What's the error?

Oh, and solve it if you want, too. It's not really that hard.

Further questions:
• Which blanks CANNOT have a prime number in them?
• Which blanks COULD have certain prime numbers?
• Which blanks essentially force this problem to be non-unique?

source.

1. Hmm, I'm not sure I've picked out what you had in mind, but it could be argued that this is a question of interpreting the puzzle. Otherwise, there are a couple of other nits I can pick, but I don't come away with a satisfying error. Perhaps that's similar to the puzzle itself which doesn't feel rewarding to have solved?

Also, being in an Asian country, I see crazy homework assignments sent around by disbelieving parents all the time. Just because some silly teacher assigns something, doesn't mean the students can do it or that it has helped them learn.

Joshua
3jlearneng.blogspot.com

2. I objected to his definition of the Order of Operations.

1. Sure. Literally following what he wrote means that you calculate 11+ab/c before you subtract that total, I guess, and that's different from how most of us would understand the puzzle.

My feeling is that order of operations is really just useful as a bar-trick: write something potentially ambiguous and then bet someone they can't do the calculation. whatever answer they give, tell them that they used the wrong order of operations.

In practical applications, it is far too dangerous to rely on everyone having the same understanding of the conventions and far too easy to add clarifying parantheses.

If my students worked on this snake puzzle, I would give them extra points for every alternative interpretation they could justify. Am I encouraging them to criticize their homework and develop into a new generation of mathematical curmudgeons? Maybe....

3. The order of operations has no natural underlying purpose ... it is merely a way to ensure that, given the same input expression, everyone will come to the same conclusion. To label it a bar-trick is to completely miss its purpose: eliminate the need for multiple nested parentheses and to get everyone on the same page. If you write 30 / 2 * 3 and we all apply the same rules, we get the same answer, 45. If you can't count on the order of operations, then you have to write (30 / 2) * 3 in order to be understood. It's got nothing to do with nit-picking.

"My feeling is that order of operations is really just useful as a bar-trick: write something potentially ambiguous and then bet someone they can't do the calculation. whatever answer they give, tell them that they used the wrong order of operations."