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1, 2, 3, 4, 5 = 2017

Can you use the digits 1, 2, 3 4 and 5 (in some order), along with common mathematical operations, to make 2017?

Allowed:
Concatenation of digits Addition, subtraction, multiplication, division Fractions
Exponents, roots
Factorials


What about just the digits 1, 2, 3 and 4? Is that enough to reach 2017?

Note by Chung Kevin
9 months ago

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\(\frac{(4+3)!}{\frac{5}{2}}+1=\boxed{2017}\)

The other case seems quite difficult; given that 2017 is a prime number.

Yatin Khanna - 9 months ago

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found more by slightly modifying your solution-

\(\dfrac{((3!)+2)!}{5 \times 4}+1\),\(\dfrac{(3!)\times(4\times2)!}{5!}+1!\)

Anirudh Sreekumar - 9 months ago

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Very similar to what I did, using 2016+1 :)

Chung Kevin - 9 months ago

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@Chung Kevin 2017, being a prime it is hard!.I've gotten to 2016 so many times like- 2016= \(2^5(4^3-1)\)

Anirudh Sreekumar - 9 months ago

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@Anirudh Sreekumar Wow! Can you add all the different ways that you found?

Chung Kevin - 9 months ago

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@Chung Kevin hey i got one more for 2017,\((5!+3!)\times 4^{2}+1\)

Anirudh Sreekumar - 9 months ago

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Works fine :)
Any ideas about the 1,2,3,4 case?

Yatin Khanna - 9 months ago

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@Yatin Khanna nope still trying :)

Anirudh Sreekumar - 9 months ago

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