I went to visit the National Museum of Mathematics (MoMath) in New York City to walk the Million Millimeter March to celebrate the 1 millionth visitor to MoMath. Puzzle enthusiast and mathematician Peter Winkler (Dartmouth) joined me to provide some fun facts about numbers along the way…

The route is shown below.

The fun facts about numbers explained by Peter Winkler are copied below for reference:

142,857 – a cyclic number. Try multiplying it by 1, 2, 3, 4, 5 or 6 and see what happens!

219,978 – the only 6-digit number such that if you multiply it by 4 it reverses!

322,560 = 9! – 8!

422,481 – the smallest number whose fourth power is itself the sum of three smaller fourth powers: 422,481^4 = 414,560^4 + 217,519^4 + 95,800^4

548,834 – a six-digit number equal to the sum of the sixth powers of it’s six digits: 548,834 = 5^6 + 4^6 + 8^6 + 8^6 + 3^6 + 4^6

604,800 – the number of seconds in a week.

742,900 – the number of different ways to walk from the bottom left to the top right (only moving along grid lines to the right or upward) in a 13×13 grid, always staying below the diagonal.

801,125 – the smallest number that is the sum of two positive squares in at least 2^2^2 ways.