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Logic Level 5

0000?=80000 \Large \underbrace{0 \quad 0 \quad 0 \quad \ldots \quad 0}_{\text{?}} = 80000

If you are only allowed to use the digit 0 and the mathematical operators like addition, subtraction, multiplication, division, exponents, factorials, multifactorials and parenthesis. What is the minimum number of 0's that I need to get the number 80000 exactly?

Details and Assumptions:

  • As an explicit example, 80000=0!×80000=0!+0!+0!++0!80 thousand 0s80000= 0! \times80000= \underbrace{0!+0!+0!+\ldots+0!}_{\text{80 thousand } 0's} . So it's possible to get the number 80000 with eighty thousand 0's.

  • You may want to familiarize yourself with multifactorial notations first.


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