James Tanton has produced another great video on this one on a very exciting partitioning problem with a very clever solution.
There are four ways to divide the number 6 in a sum of distinct figures: 6 = 5 + 1 = 4 + 2 = 3 + 2 + 1. There are four ways to divide the number by 6 in odd numbers: 5 + 1 = 3 + 3 = 3 + 1 + 1 = 1 = 1 + 1 + 1 + 1 + 1 + 1. It is no coincidence that the number of ways are the same. In 1740 proved Euler, it will always be so! His evidence is inventive, and here it is! I have also added a challenge at the end to discover other bizarre results such as this. (I bet you can do it!)
I thoroughly enjoy the Royal ability to find interesting problems and make them available for those of us who are not professional mathematicians. In fact, all the Royal videos available for motivated high school students.
I was pleased to see Mr. Tanton included in Math Pickle page inspired people.
A MathPickle lighthouse to the core-James Tanton is a fully fledged mathematician with a fantastic website offering videos for school teachers and first year of university teachers. Visit his site here.
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