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In the realm of mathematics, we seldom present school-aged students with problems that remain unsolved. Traditionally, such challenges are deemed too advanced for young learners. However, Math Pickle gathered together mathematicians to curate a list of 13 unsolved math problems, tailored to be accessible for students from kindergarten through grade 12. These intriguing puzzles are crafted to be age-appropriate and stimulating, engaging young minds in creative problem-solving endeavors.

I've been playing around with some of these problems in my classes these past couple weeks, with some really interesting results.  There's something enticing about working on a problem that doesn't yet have a solution, and it's been engaging the imaginations of some of my students.  Here are some of the benefits to having school-aged children grapple with unsolved math problems.

Students become more creative as they explore non-traditional methods, an essential skill for modern careers.

When playing around with problems that don't have a known solution, students know they can't try a combination of the skills they've already learned in order to find an answer.  They need to try other techniques that they haven't yet thought about.  This creativity in thinking through math problems is one of the skills that 21st century jobs are looking for.  Interview questions in the engineering, business and technology fields tend to have interesting problem-solving questions, where the interviewers are looking for creativity, because hiring teams know that these skills are essential for the work of their employees.  Working with unsolved problems can help develop these skills in students.  

Students break down the problem for themselves into manageable pieces, building their organization skills.

Last week, I presented the Cookie Monster problem to some 8th graders. The problem goes like this: Cookie Monster wants to empty his jars of cookies in as few days as possible. He can only eat the same number of cookies from any combination of jars each day. The challenge is to figure out the optimal way for him to do so, regardless of the number of cookies.

Knowing they couldn't tackle the whole problem at once, my students found the greatest number of days it would take the Cookie Monster to eat cookies out of a certain number of jars, and they also found the smallest number of days for different numbers of jars.  What makes this impressive is that these answers hold true regardless of the number of cookies in each jar.  It was also a first step in solving the entire problem, and became a satisfying milestone along the way.  

Students develop patient problem solving and collaboration skills, transferable skills that are applicable in all aspects of life.  

Since there is no known right answer, it's clear to students that they probably won't find an answer quickly and easily.  Knowing this, they give themselves permission to try things that they feel are potentially absurd, and work together, bouncing ideas off each other and getting things wrong.  

One unsolved problem that some of my 7th graders have been working on is called Boomerang Fractions.  Starting with 1, we can either add a specific unit fraction or take the reciprocal of the previous fraction to return to 1. The goal is to find a pattern to achieve this in the shortest number of steps for fractions of the form 1/n.

Finding even one sequence takes a while.  Classes of students split up the fractions and each tried to solve a couple of them, then combined their results and looked for patterns.  So far, some of them have managed to find patterns for 1/n where n is a prime number.  Now they're working on patterns in composite values for n.  

Unsolved problems require creativity and ingenuity, not simply memorizing algorithms.  At their core, this is what mathematics is – the discovery of new patterns using imagination and logical reasoning.  I'm looking forward to seeing what other benefits this type of deep thinking and logical reasoning these problems can create!