# The Red Box Challenge

Here is another hundreds chart that I created in PowerPoint. This is the Light Switch Hundreds Chart. Can you explain why it arrives at the final set of numbers? Try to think outside of the “box.” You’ll understand what I mean in just a moment…

**Update: This challenge has been solved one time now. Congratulations to Rik Rowe’s High School Math Class in Massachusetts who have been the first to solve. Thanks @whsrowe for challenging your class and for sending me the answer. I am very impressed. The challenge remains extended to all others. Can you explain why this is true? **

If you would like to download your own copy of an interactive hundreds chart, click here.

Extension problem: would it still be the perfect squares if you click on every multiple and not just the first ten multiples?

I was hoping someone would ask that very question! As food for thought, if you clicked on multiples of 11, I don’t think it would erase any of perfect squares, so they would still stand. However, it would “clutter” the chart with some additional numbers. So that makes me wonder what it is about 10 that is unique. The one piece that catches my attention is that I chose to use the first 10 multiples of each number. What would have happened if I chose the first 9 multiples of each number, or the first 5 multiples, or the first 12 multiples.

Nice question!

Absolutely love it!!! Is there a downloadable version of the lights table?

Hi, Dean. I don’t have a downloadable version, but your comment has encouraged me to set one up. I think that will be my next step.

yes! please do!

I have taken your excellent idea and put it into code that lives on the web: no downloads or plug-ins to slow it down. Hope someone finds it useful! http://www.scienceoftech.net/HundredsChart.php ( It’s a modification of the Animated Multiplication Table I shared earlier…)

My son and I watched the video and talked about the pattern. He immediately noticed those numbers had something to do with the multiplication table he learned/talked about in 3rd grade. I teach 1st and love math. My son is in 6th grade and loves math too. Those numbers are squares of the numbers 1-10. Twitter handle @teachjwright

Great catch, Jeanne. Yes, they are all square numbers. I’ll add some more information below to explain why that is…

***SPOILER ALERT***

The numbers keep turning on an off every time they are clicked. 1 click turns them to red… 2 clicks turn them back to white… an odd number of clicks turns the light red …an even number of clicks turns the light back to white.

Many numbers have an even number of unique factors. Square numbers have an odd number of unique factors. So square numbers have lights that remain red after all of the factors are depleted.