Can You Work Out These 4 Math Questions While Running A 42.2 km Marathon?

4 Last Unknown Kilometers Left, Can You Work Them All Out?

Earlier in Kaohsiung’s Meinong district, organizers of the 147-kilometer “Good Rice” Super Marathon posted calculus and other math puzzles on utility poles along the route — complete with a line of Zhuyin symbols that secretly spell out each answer.

Some runners sprint, some keep a steady pace, and some jog to enjoy the scenery. By solving a quick problem, runners are encouraged to slow down, engage their minds, and appreciate Meinong’s landscape. Though some joked they’d need a calculator, or feared the puzzles might prevent them from finishing, many competitors had already seen the questions (which were leaked on Facebook) and worked out the answers in advance.

Each of these 4 expressions requires only basic high school calculus and algebra knowledge, so if you’ve got a sharp mind and an abled body, you might be able to crack these in your head while running a 42.2 km marathon.

So let’s take a look at each of these 4 expressions.

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Sî-kân kò, màn-màn suàn: Time’s enough, go slowly

The first ever mathematical sign we see on the race features a standard definite integral.

It’s really quite simple. Let’s solve for the indefinite version first.

Then we substitute in the limits.

Well done! You’ve got only 8 kms to go. You got this!

Keep going, keep running.

時間夠，慢慢算: There’s plenty of time, take your time calculating

To understand this infinite summation, we have to take a look at one of the classic Taylor expansions for the inverse of the tangent function, which is

It converges absolutely for |x| ≤ 1.

Now when we plug in x = 1, the series becomes

We know from high school trigonometry that arctan(1) = π/4, therefore

And upon multiplying by 4, there are

3.1415926 … kms left in your race! Let’s push for the final pi(e)!

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Sî-kân kò, màn-màn suàn: Time’s enough, go slowly

This one is in my opinion the hardest expression in this marathon race. Because at first glance, as x approaches π, it might see that the limit of the expression is 0.