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A friend of mine shared a puzzle with me this evening.

Using the numbers 1, 1, 5 and 8 exactly once, and the basic operations (+, -, /, *) and (optionally) parentheses, form an expression which has the value 10.

No trickery involved (use base 10, and concatenation of numbers is not allowed).

It should be quite simple for the math wizards here; I was able to solve it quickly because I had a hunch the solution would be the same as for a similar problem, which I already knew the solution to. This is either a hint or a bonus problem:

Make 24 out of 1, 3, 4 and 6 (same rules apply as above).

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  • $\begingroup$ The bonus is part of The $24$ Game. $\endgroup$
    – Mr Pie
    Jul 27, 2018 at 15:30

2 Answers 2

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Beautiful, I found them.

First one:

$\dfrac{8}{1-\frac{1}{5}}$

Second one:

$\dfrac{6}{1-\frac{3}{4}}$

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A less sophisticated solution would be

$10 = 8 + 1 + 1^5$

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  • $\begingroup$ Oops, not the basic operations only $\endgroup$
    – Bernhard
    Jun 11, 2017 at 9:03
  • $\begingroup$ yes; it's not a difficult puzzle but not that easy. $\endgroup$
    – Glorfindel
    Jun 11, 2017 at 9:08
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    $\begingroup$ Also slightly cheating is $1.8\times5+1$ $\endgroup$
    – Ian Miller
    Jun 11, 2017 at 12:09
  • $\begingroup$ Similar answer, invalid for the same reason, would be 5*(1^8+1) $\endgroup$
    – Daniel Schepler
    Jul 27, 2018 at 17:26

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