Noted

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.)

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