IBM Research | Ponder This | December 2015 solutions
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December 2015

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Several solvers implemented a lookup table in three operations, like Dan Dima's solution
(90089088087086085084083000000000000000000000000082081080079078077076075074000000000000000000000073072071070069068067066065000000000000000000000000000000000000000000000000000000000000000000000122121120119118117116115000000000000000000000000114113112111110109108107106000000000000000000000105104103102101100099098097000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 / (1000 ** x)) modulo 1000.

Septimus G. Stevens VII suggested a smaller lookup table: x - (9592598315813 % (81 + (x & 112))).
Motty Porat used a similar approach with only 3 operations: x - (309276143438415101 mod (x | 1039)).
Yan-Wu He proposed another solution: ((0x010101010101 * x) & 0x20300080F0BF) modulo 513.