# Challenge

This is a challenge to all the Brilliant members. Using symbols make your answer to the question as 6. You can use symbols such as squares, plus, minus etc. An example of $$6$$ is been done for you.

$$0 0 0 = 6$$

$$1 1 1 = 6$$

$$2 2 2 = 6$$

$$3 3 3 = 6$$

$$4 4 4 = 6$$

$$5 5 5 = 6$$

$$6 + 6 - 6 = 6$$

$$7 7 7 = 6$$

$$9 9 9 = 6$$

And finally $$8$$ is toughest number where you have to use all the Symbols that you have used in all the above questions.

$$8 8 8 = 6$$

4 years, 10 months ago

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I'll post the first one: $$(0!+0!+0!)! = 6$$

All right, I'll post the "hard one": $$(\sqrt { \frac { 8 }{ \sqrt { .\dot { 8 } } \sqrt { .\dot { 8 } } } } \quad )!=6$$.

Note that $$.\dot { 8 } =0.888888....$$

- 4 years, 10 months ago

Correct! But for $$8$$ you made it quite difficult. In a simpler way it can be $$8 - \sqrt{\sqrt{8+8}}=6$$. And for $$0$$ it can also be $$(\cos0+\cos0+\cos0)!=6$$.

- 4 years, 10 months ago

Well, you threw me off by saying it's so difficult!

- 4 years, 10 months ago

No, you made it little complex

- 4 years, 10 months ago

No, you said it was "toughest" and so I figured that only a tough answer would do. How was i to know that a simpler answer was possible? ??

If nobody else comes up with any of the other answers, I'll post them all pretty soon.

- 4 years, 10 months ago

don't tell me that you have taken it from scam school

- 4 years, 10 months ago

$$(0!+0!+0!)!=6$$

$$(1+1+1)!=6$$

$$2+2+2=6$$

$$(3\times 3)-3=6$$

$$(4-(4\div 4))!=6\quad or\quad 4+4-\sqrt { 4 } =6$$

$$5+(5\div 5)=6\quad or\quad { (5 }^{ 2 }+5)\div 5=6$$

$$7-(7\div 7)=6\quad or\quad { (7 }^{ 2 }-7)\div 7=6$$

$$(\sqrt { 8+(8\div 8) } )!=6\quad or\quad 8-\sqrt { \sqrt { 8+8 } } =6$$

$$(\sqrt { ((9\times 9)\div 9) } )!=6$$

- 4 years, 9 months ago