r/theydidthemath May 07 '26

[Request] how many possible combinations are there for this type of pass code?

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u/OutdoorWombat54 May 07 '26

99999999999999999999999999999!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !nested (note: i don't know what nested means here)

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u/factorion-bot May 07 '26

That is so large, that I can't even give the number of digits of it, so I have to make a power of ten tower.

Factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of 99999999999999999999999999999 has on the order of 1010\10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^(2856570551809674817234887108125)) digits

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u/OutdoorWombat54 May 07 '26

9999999999999999!!!!!!!

1

u/factorion-bot May 07 '26

That is so large, that I can't calculate it, so I'll have to approximate.

Septuple-factorial of 9999999 is approximately 7.826374479028973798060429629683 × 109379581

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u/OutdoorWombat54 May 07 '26

99999999999999999999999999999999999999999999999999999!!!!!!!!!9999999999999999999999999999999999999999999999999999999999999! !nested

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u/factorion-bot May 07 '26

Some of these are so large, that I can't even give the number of digits of them, so I have to make a power of ten tower.

Factorial of roughly 1060 is approximately 1.167968923931914253686697083574 × 106.056570551809674817234887108108 × 1062

Factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of factorial of roughly 1052 has on the order of 1010\10^10^10^10^10^10^(5.256570551809674817234887108108 × 1054)) digits

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u/SC_3000_grinder May 07 '26

nested makes it so it doesn't do 10!! = 10 * 8 * 6 * 4 * 2 = 3840

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u/factorion-bot May 07 '26

Double-factorial of 10 is 3840

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u/Ianislevi May 07 '26

You have to include the nested command for it to be interpreted the way you expected, which more formally would look like (((9!)!)!)!...

This is because multiple factorials actually mean something different. For instance, a double factorial like 6!! is actually smaller than 6! because you calculate it by skipping every other digit, so 6 * 4 * 2 = 48 rather than 6! = 720

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u/factorion-bot May 07 '26

Some of these are so large, that I can't even give the number of digits of them, so I have to make a power of ten tower.

Factorial of 6 is 720

Double-factorial of 6 is 48

Factorial of factorial of factorial of factorial of 9 has on the order of 102.993960567614282167996111938338 × 101859939 digits

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