A curiosity from DePauw University mathematician Underwood Dudley: Arrange the six permutations of 1, 2, 3 in ascending order and find the differences of successive pairs:
123 132 213 231 312 321
9 81 18 81 9
The top row totals 1,332, the bottom row 198. Arrange the first nine digits of π in triplets and add 198 to each:
314 159 265 198 198 198 --- --- --- 512 357 463
The three sums total 1,332.
(Underwood Dudley, “What to Do When the Trisector Comes,” Mathematical Intelligencer 5:1 [March 1983], 20-26, via Martin Gardner’s Whys & Wherefores, 1989.)



