Simple number puzzle

You have to solve the following:

00 _ 00 _ 0=60 = 6

11 _ 11 _ 1=61 = 6

22 _ 22 _ 2=62 = 6

33 _ 33 _ 3=63 = 6

44 _ 44 _ 4=64 = 6

55 _ 55 _ 5=65 = 6

66 _ 66 _ 6=66 = 6

77 _ 77 _ 7=67 = 6

88 _ 88 _ 8=68 = 6

99 _ 99 _ 9=69 = 6

You can put as many operations in the spaces but they must not contain a digit/letter. e.g.

You can have 2×2+2!2 \times \sqrt{2} + 2! but not 22+23+2e2^2 + \sqrt [3]{2} + 2e.

You can only use factorials and double factorials, BODMAS/PEMDAS operations and square roots.

Good luck.

Extension: Find the smallest positive integral value of nn such that nn _ nn _ n=6n = 6 has no solutions.

Note by Sharky Kesa
4 years, 9 months ago

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1 vote

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Answer below. If you want to do it yourself, don't scroll down: .............................................................................. (0!+0!+0!)!(0!+0!+0!)!

(1+1+1)!(1+1+1)!

2+2+22+2+2

3!+333!+3-3

4+4+4\sqrt { 4 } +\sqrt { 4 } +\sqrt { 4 }

(5÷5)+5(5\div5)+5

6+666+6-6

7(7÷7)7-(7\div7)

(8+8!÷8)!\left( \sqrt { 8+8 } !\div 8 \right) !

9+9×9\sqrt { 9 } +\sqrt { \sqrt { 9 } \times \sqrt { 9 } }

Legid?

Julian Poon - 4 years, 9 months ago

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Nice!...

Jeremy Bansil - 4 years, 9 months ago

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You should try it yourself! Its fun! :D

Julian Poon - 4 years, 9 months ago

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Ahh... but that was only the first part o the problem. You have to find as many different solutions as you can.

Sharky Kesa - 4 years, 9 months ago

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Try this

9 9 _ 9 9 _ 9=109 = 10

Without addition.

Krishna Sharma - 4 years, 2 months ago

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(9÷99)-(-9\div9-9)

Julian Poon - 4 years, 2 months ago

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@Julian Poon Sir, you are genius!

Krishna Sharma - 4 years, 2 months ago

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@Krishna Sharma But -- is ++...

Julian Poon - 4 years, 2 months ago

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@Julian Poon Try the extension.

Sharky Kesa - 4 years, 2 months ago

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@Sharky Kesa After the crazy logiclogic question by π\pi... I'd rather not

Julian Poon - 4 years, 2 months ago

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@Julian Poon Why? Those questions are awesome. Plus, this question shouldn't be too difficult.

Sharky Kesa - 4 years, 2 months ago

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