## Friday, December 25, 2015

### Don't freak if you can't solve a math problem that's gone viral by Kevin Knudson

 Photo: Kevin Knudson
"They're easier than you think." according to Kevin KnudsonProfessor of Mathematics, University of Florida.

It's been quite a year for mathematics problems on the Internet - three questions have been online everywhere, causing consternation and head-scratching and blowing the minds of adults worldwide as examples of what kids are expected to know these days.

As a mathematician, I suppose I should subscribe to the 'no such thing as bad publicity' theory, except that problems of this ilk a) usually aren't that difficult once you get the trick, b) sometimes aren't even math problems and c) fuel the defeatist 'I'm not good at math' fire that pervades American culture.

The inability to solve such a problem quickly is certainly not indicative of a person's overall math skill, nor should it prompt a crisis of confidence about the state of American math aptitude.

When is Cheryl's birthday?
In April, the Internet erupted with shock that 10-year-olds in Singapore were asked to answer the following question on an exam.

 The logic puzzle from the Singapore and Asian Math Olympiads.

Except that it wasn't for elementary school students at all; rather it appeared on an Asian Olympiad exam designed for mathematically talented high school students. What's more, this isn't even a math problem, but a logic problem. It's true that students tend to learn formal logic via mathematics (plane geometry in particular), so it is common to see problems of this type in mathematics competitions.

When I was in junior high, we spent a good deal of time on these puzzles in my language arts class, and I met them again when taking the GRE prior to entering graduate school (the test contains a whole section of them). If you're stumped, check out a solution to the problem.

Vietnamese eight-year-olds do arithmetic
A month later, we heard about a third grade teacher in Vietnam who set the following puzzle for his students. Place the digits from one to nine in this grid, using each only once (the : represents division).

 A puzzle for Vietnamese children. VN Express
This reminds me of the (probably apocraphyl) story of one of the greatest mathematicians in history, Carl Friedrich Gauss. Legend has it that when Gauss was seven or eight, his teacher, wanting to occupy his students for a while, told the class to add up the numbers from 1 to 100. Gauss thought about it for 30 seconds or so and wrote the correct answer, 5,050, on his slate and turned it in.

The puzzle above has a similar feel. It's really a question about knowing the order of arithmetic operations (multiplication/division, addition/subtraction, in that order). Beyond that, it just takes trial and error; that is, it's kind of just busy work. Someone who knows some algebra might be able to generate some equations to gain insight into how you might find a solution.

Another approach would be to open up a spreadsheet program and just try all the possibilities. Since there are nine choices for the first box, then eight choices for the second, and so on, there are only (9)(8)(7)(6)(5)(4)(3)(2)(1) = 362,880 possible configurations, of which only a few will give a valid equation. This can be programmed with very little effort.