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Can you find a way to make:

$5\ 5 \ 5 \ 5 = 19$

by adding any operations or symbols? You can use only these symbols:

$+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$.

It is limited to this list, and concatenation is also allowed. You cannot add other numbers to the equation.

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. If you have legitimate questions about the puzzle statement, including allowed operations and the like, ask them (to the OP) or include your assumptions in your answer as others have done; debating them with other users is a fairly fruitless exercise, and not what comments are for in any case. $\endgroup$
    – Rubio ♦
    Commented Aug 28, 2018 at 14:58
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    $\begingroup$ The amount of solutions is likely to be too big. I am not sure if answers putting operations between 1 and 9 are valid. BTW, came up with different solution which is, I guess, uninteresting (because there already are too many) and anyway I can't post an answer. $\endgroup$
    – rus9384
    Commented Aug 28, 2018 at 19:38
  • $\begingroup$ There are lots of possible solutions for this question. A lot of good answers have been given too. It would be nice if one got accepted and the question closed or else it feels like it is too broad with a lot of correct answers. $\endgroup$
    – R.D
    Commented Aug 29, 2018 at 12:05

10 Answers 10

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Here's one way I found:

$\dfrac{5!-(5\times 5)}{5}=19$

Or, using just the characters explicitly allowed in the question:

(5! - (5 * 5)) / 5 = 19

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  • $\begingroup$ Somebody upvote once more (I already have)! It's a great answer and @Riley's nearly on $10k$ reputation! :D $\endgroup$
    – Mr Pie
    Commented Aug 29, 2018 at 15:04
  • $\begingroup$ @user477343 Thank you! I will now use my powers responsibly. $\endgroup$
    – Riley
    Commented Aug 29, 2018 at 17:04
  • $\begingroup$ Well, after those Riley riddles you made, I think you quite deserve it :) $\endgroup$
    – Mr Pie
    Commented Aug 29, 2018 at 21:41
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If the double factorial is allowed, then I propose

$$5!!+5-5/5$$

WolframAlpha agrees that the result is 19.

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31
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I am quite sure it is not the expected answer but it is the immediate answer comes into my mind.

$\frac{5+5}{5+5}=1^9$

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    $\begingroup$ I like this one (+1), as my immediate answer (with fewer symbols) would be similar, alternating division and multiplication, while keeping the same right-hand side as yours. (Meta: I'm not writing my solution in the comment in order to avoid spoiling, as rot13 wouldn't work here. Not sure what is the standard policy in this case. Should I post it as a separate answer?) $\endgroup$
    – Maiaux
    Commented Aug 27, 2018 at 16:06
  • $\begingroup$ @Maiaux if it is really similar, do not post it as a seperate answer. This has happened before here, where a user deleted his/her answer (I won't name who, exactly) for its similarity compared to another answer. $\endgroup$
    – Mr Pie
    Commented Aug 29, 2018 at 15:06
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For the 5s

$$\left(5 - \frac55\right)! - 5 = 19 $$

For the 1s (previous edit)

$$(1+1+1)!-1=5$$

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My way:

$(5+5)\times\frac55=1+9$

and

$(5+5)-\frac55=1\times9$

New, and added for it's simplicity:

$5+5+5-5=1+9$

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16
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In base-11, the trivial addition works:

$$ 5_{11} + 5_{11} + 5_{11} + 5_{11} = 19_{11} $$

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    $\begingroup$ Those subscript 1s could be considered other numbers? $\endgroup$
    – Viktor Mellgren
    Commented Aug 27, 2018 at 8:54
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    $\begingroup$ just remove the subscripts they are not needed (can we not as usual ignore the number base). $\endgroup$
    – ctrl-alt-delor
    Commented Aug 27, 2018 at 9:04
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5555 != 19 : Credit : Jonathan Allan

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    $\begingroup$ Is this now an equation? $\endgroup$
    – ctrl-alt-delor
    Commented Aug 27, 2018 at 9:05
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From the comment above

5555 ≠ 19

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One way to think of it -

19 HEX = 25 DEC

Therefore -

$\frac{ 5 }{ 5 } * 5 * 5 = 25$

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(5! - 5 * 5) / 5 = 19
(120 - 25) / 5 = 19
95 / 5 = 19

or

5 + 5 + 5 - 5 = 1 + 9

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