Puzzles & Quizzes

Can You Solve This Tricky Math Problem for 8-Year-Olds?

It's a parental nightmare not to be able to figure out your kid's math homework, especially when they're in elementary school. Yet that's exactly what went down for one mother — and a slew of other confused internet users — last month. The problem, originally posted as a photo on the parents' forum Mumsnet, may be a little more difficult than you'd expect an 8-year-old student to be assigned in class.

Scroll down to read the problem and the solution. No judgment if it trips you up a bit.

Here's the Problem

On the coast, there are three lighthouses.

The first light shines for three seconds, then is off for three seconds.

The second light shines for four seconds, then is off for four seconds.

The third light shines for five seconds, then is off for five seconds.

All three lights have just come on together.

When is the first time that all three lights will be off together?

When is the next time that all three lights will come on at exactly the same moment?

Give this math problem a shot, then scroll down for the answer.

Here's the Answer

To be fair, the problem isn't calculus. But for a third-grader — or maybe even you! — it might as well be. If you're struggling with this problem, don't feel bad. The first comment on this Mumsnet thread is: "That is a ridiculous question and I'm only here to learn something." Here's a helpful hint as you try solving it: Try drawing out timelines for the lights, or even a grid with rows representing the lights and when they are on and off.

Ready for the answer? If you drew a little diagram or timeline, you can see that the first time all the lights are off at the same time is six seconds after they were all turned on. To find out the next time all three lights will flicker on at exactly the same moment, we need to know how often each one comes on. Given how long each light shines, we know that the first light comes on every six seconds, the second every eight, and the third every 10. We can find out when they will all come on together by determining the lowest number that can be by divided by all of those numbers: 6, 8, and 10. That time would be 120 seconds, or two minutes, after first turning the lights on. Did you get it?

Want more? Check out puzzle master Alex Bello's "Can You Solve My Problems?: Ingenious, Perplexing, and Totally Satisfying Math and Logic Puzzles." We handpick reading recommendations we think you may like. If you choose to make a purchase through that link, Curiosity will get a share of the sale.

Written by Joanie Faletto June 11, 2018

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