How many 6's are in 27?

Logic Level 4

You have been challenged by a friend to make the number 27 using the digit 6 (as many times as you want). What is the minimum number of 6's that is required?

Allowed operations:

  • + , , × , ÷ , +, -, \times, \div, \sqrt{ \cdot }
  • Brackets
  • Factorial
  • Power / Exponentiation
  • Concatenation of 6's in the expression

Disallowed operators. Everything else, including but not limited to:

  • Flipping the 6 into a 9
  • Decimal points (since you need a concatenate a 0)
  • Other mathematical operators like cube roots

An example of how to use these operators is using 4's to create 28 would be 28 = 4 × ( 4 + 4 + ( 4 ÷ 4 ) ) 28=4 \times (4+\sqrt{4}+(4 \div 4)) , which uses five 4's, but you can also do this with two 4's as follows: 28 = 4 ! + 4 28=4!+4 .

5 3 7 4 6

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1 solution

Sharky Kesa
Nov 25, 2016

This is the best solution I got, and I doubt there is a better solution:

27 = ( 6 6 + 6 ) 6 \large 27 = \left ( \dfrac {6}{\sqrt{6+6}} \right )^6

How about this? (Only 3 sixes! :) )

27 = 6 . 6 + 6 ! 27 = \sqrt{\frac{6}{.\overline{6}} + 6!}

Geoff Pilling - 4 years, 6 months ago

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Or how about 2 sixes? (One is just upside down) :0)

27 = 9 + 6 ! 27 = \sqrt{9 + 6!}

Geoff Pilling - 4 years, 6 months ago

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ahah! You've found a loophole! Sharky, you should say that you can't turn the 6 upside down

Pi Han Goh - 4 years, 6 months ago

Fixed both issues... Better?

Sharky Kesa - 4 years, 6 months ago

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@Sharky Kesa Ok, fair enough... But I would still claim that the bar over the six is considered a mathematical symbol. (Like the decimal point)

Geoff Pilling - 4 years, 6 months ago

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@Geoff Pilling The decimal point is dis-allowed.

Sharky Kesa - 4 years, 6 months ago

That goes against the rules right?

dishith borra - 1 year, 11 months ago

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No. \quad

Pi Han Goh - 1 year, 11 months ago

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You are wrong

dishith borra - 1 year, 10 months ago

Yes it does, it says in the rules you can't add a decimal point or flip it around

dishith borra - 1 year, 11 months ago

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Yeah. I think the rules were updated after I made my post. But, agreed, under the current rules neither of my answers would qualify.

Geoff Pilling - 1 year, 10 months ago

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