I really enjoyed and recommend the article by Lazebnik, which can be found at http://www.math.udel.edu/~lazebnik/papers/surprises.pdf <http://www.math.udel.edu/~lazebnik/papers/surprises.pdf>. It never goes outside undergrad math, maybe never beyond sophomore math. But it has a lot of things I hadn't heard before, including a number of interesting unsolved problems. —Dan
On Oct 7, 2016, at 12:53 PM, James Propp <jamespropp@gmail.com> wrote: . . . . . . . . . an article in Mathematics Magazine
(Vol 87, No 3, June 2014) called "Surprises, Surprises, Surprises", written by Felix Lazebnik. Lazebnik's statement is slightly more general: "Consider any positive integer N whose (decimal) digits read from left to right are in non-decreasing order, but the last two digits (tens and ones) are in increasing order. Prove that the sum of digits of 9N is always exactly 9."
. . . . . .