4
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  • You must use all four 4s.

  • You may use addition (+).

  • You may use subtraction (-).

  • You may use multiplication, such as with asterisks (*) and/or grouping symbols.

  • You may not use any division.

  • You may not use decimal points.

  • You may not use any concatenation.

  • You may use grouping symbols, such as parentheses and/or brackets.

  • You may not use any type of factorial signs.

  • You may use up to four square root symbols, including the use of nested square roots.

  • You may not use exponentiation.

  • You may not use logarithms.

  • You may not use trigonometric functions.

  • You may not use any other numbers, characters, or operations, to include no other roots.

  • This is in base 10.

Try to create and post 10 additional --> essentially <-- different solutions.

Permutations are the same.

This was moved to this site, because it is a math puzzle.

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2 Answers 2

8
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I think these are all essentially different and within the rules

1. $\sqrt{4} + 4 + 4 - 4 = 6$
2. $\sqrt{4} + 4 + \sqrt{4} - \sqrt{4} = 6$
3. $\sqrt{\sqrt{4\times 4}} + \sqrt{4 \times 4} = 6$
4. $\sqrt{\sqrt{4\times 4}} +\sqrt{4} + \sqrt{4} = 6$
5. $(\sqrt{4} \times 4) - 4 + \sqrt{4} = 6$
6. $\sqrt{4 \times 4 \times 4} - \sqrt{4} = 6$
7. $\sqrt{4 \times 4} + 4 - \sqrt{4} = 6$
8. $((4-\sqrt{4}) \times 4) - \sqrt{4} = 6$
9. $\sqrt{\sqrt{4 \times 4} \times 4} + \sqrt{4} = 6$
10. $\sqrt{4+4-4} + 4 = 6$

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1
  • $\begingroup$ I may post some additional solutions tomorrow. $\endgroup$ Jan 17 at 2:01
2
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These are some additional solutions:

  1. $ \ \sqrt{\sqrt{4\sqrt{4*4 \ } \ } \ } \ + \ 4 = \ 6$
  2. $ \ 4\sqrt{4} - \sqrt{\sqrt{4*4 \ } \ } = \ 6$
  3. $ \ 4 + 4 - \sqrt{\sqrt{4*4 \ } \ } = \ 6$
  4. $ \ \sqrt{(4 + \sqrt{4})(4 + \sqrt{4}) \ } = \ 6$
  5. $ \ \sqrt{ \sqrt{4 \ }(4*4 + \sqrt{4 \ }) \ } = \ 6$
  6. $ \ \sqrt{4*4\sqrt{4} + 4 \ } = \ 6$
  7. $ \ 4 + \sqrt{\sqrt{4 \ }(4 - \sqrt{4 \ }) \ } = \ 6$
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