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What is the Open Problem Challenge?


Open problems are problems for which a solution is not yet knownWe love open problems and favor introducing young students to them as long as their formulation is easy to understand.


Our plan is to select and share one or two problems per year at the beginning of each year. We encourage teachers to share these problems with their students and friends, and to also work on them themselves. Contact us with questions and potential solutions to


If publishable results come out of the exchanges between members of the general public and CYFEMAT, the researchers involved will share the credit, following standard academic protocols.


Enjoy the first problem!


What is the minimal number of squares needed to tile an m x n rectangle, where m and n are integers?

For example, if f(m,n) is this minimal number, then f(2,3)=3 and f(5,6)=5, as shown below. Notice that the case in the middle is not minimal for a 5x6 rectangle.

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  • Click on the image above to see the problem as a Google Slides file in English, Spanish, and Portuguese.

  • Click here to see the handout we used at a session for the University of Florida Math Circle.

  • Click here to access and contribute to a document with some results.

  • For more open problems suitable for K-12 students, visit

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