TITLE: A factorian is a number equal to the sum of the factorials of its digits, e.g., 145 = 1! + 4! + 5! and 40,585 = 4! + 0! + 5! + 8! + 5!. Let F be the largest factorian. Here I provide a very simple proof that F < 2,000,000.
AUTHOR: @games_to_change
#QUARK
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P.S. Interested readers can build on this argument to show that F < 1,500,000. Hint: F’s last digit cannot be “9” unless it contains a “1” or “0” and at least two more digits less than “5”.
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Well, actually 7×9!=2 540 160
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But it still works since:
2×5!×5×9!=1 814 522. -
Oops, that's embarrassing! This came from a longer reply I gave a while back https://twitter.com/games_to_change/status/941319625626746880 …. It looks like I somehow dropped a step when condensing it to the three-tweet format. Anyway, here's my correction (reflecting the way I originally did it; your way works too) 1/2
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Of course we could (by exhaustion) but F is mathematically speaking not a very interesting number. I guess the goal of this "problem" was to demonstrate the efficiency of simple arguments.
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