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82 arithmetic/digits/sum.of.digits.p




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This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

82 arithmetic/digits/sum.of.digits.p


Find sod ( sod ( sod (4444 ^ 4444 ) ) ).

arithmetic/digits/sum.of.digits.s

let X = 4444^4444

sod(X) <= 9 * (# of digits) < 145900
sod(sod(X)) <= sod(99999) = 45
sod(sod(sod(X))) <= sod(39) = 12

but sod(sod(sod(X))) = 7 (mod 9)

thus sod(sod(sod(X))) = 7

 

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