# 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.

$8 8 8 = 6$ 6 years, 4 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 $.\dot { 8 } =0.888888....$

- 6 years, 4 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 $(\cos0+\cos0+\cos0)!=6$.

- 6 years, 4 months ago

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

- 6 years, 4 months ago

No, you made it little complex

- 6 years, 4 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.

- 6 years, 4 months ago

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

- 6 years, 4 months ago

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

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

$2+2+2=6$

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

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

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

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

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

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

- 6 years, 3 months ago