Math on the Beach

Simon doing math everywhere.

And he showed me this beautiful trick of two rows adding up to equal numbers and their squares adding up to equal numbers. And the two rows below? Even their cubes!

Now, can you come up with two rows in which also the fourth powers add up to equal sums?

Simon learned this trick from Matt Parker: you should pick numbers up to n-1, where n is the next power of 2. In this case, n would be 2 to the fifth power and that is 32, so we pick numbers up to 31. Then we write them down in two rows in such a way that the top row only has numbers whose binary expressions have an even number of ones and the bottom row – only odd number of ones.

Simon also came up with an interesting fact about the trick using a pattern of “buckets” turned in opposite directions:

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