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1-100 Composite Connector Challenge

This is a challenge for a class that has nothing to do except rejoice in connecting numbers that share common prime factors. The highest score that I've managed is 195, but I don't use computers so this can almost certainly be beaten. What I like about the challenge is that you can strategically think how to get a higher score.

Print out a 10 by 10 puzzle-sheet here - or just use standard graph paper. Then start adding the numbers 1-100. Here we have added 15 and 45. It is good that we have placed them together because they share a common prime factor.

We get 1 point because these neighbours share a common prime factor of 5.

We get an additional point because they also share a common prime factor of 3.

How many points do we get for adding the 60?

We get three points for the common prime factors of 2, 3, and 5 between 30 and 60.

Spoiler Alert: Do not keep going without trying this challenge.

I decided to start by grouping the big primes over 50 together at the bottom. I then decided to focus on getting an even region (red) a multiple of 3 region (orange) and a multiple of 5 region (yellow).

This was the best I did in an hour of play.  I'm a mathematician so I don't expect too many of your students to come close, but the classroom discussion should get interesting. On the other hand, you may beat me 😉 That humiliation would be a joy to hear!

Good luck!

1-100 Composite Connector Challenge

(MathPickle, 2012)

Standards for Mathematical Practice

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

MP1 Toughen up!

Students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

MP2 Think abstractly!

Students take problems and reformat them mathematically. This is helpful because mathematics lets them use powerful operations like addition.

MP3 Work together!

Students discuss their strategies to collaboratively solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

MP4 Model reality!

Students create a model that mimics the real world. Discoveries made by manipulating the model often hint at something in the real world.

MP5 Know the tools.

Students master the tools at their fingertips - whether it's a pencil or an online app. 

MP6 Be precise!

Students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

MP7 Be observant!

Students learn to identify patterns. This is one of the things that the human brain does very well. We sometimes even identify patterns that don't really exist 😉

MP8 Be lazy!?!

Students learn to seek for shortcuts. Why would you want to add the numbers one through a hundred if you can find an easier way to do it?


Please use MathPickle in your classrooms. If you have improvements to make, please contact me. I'll give you credit and kudos 😉 If you are using MathPickle with adults, please mention the website. If you are from a private school, please ask parents or administrators to donate.

Gordon Hamilton

(MMath, PhD)