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Rules:

  1. All 3 digits — $3$, $3$, and $5$ — must be used once each in any order. You can concatenate these digits to create multi-digit numbers (i.e. $33$).
  2. You can use the factorial operation ($n!$), the subfactorial operation ($!n$) and the double factorial operation ($n!!$) (i.e. $3!=6$, $!5=44$, $(3!)!!=48$). However, extended multi-factorials ($n!!!...$) cannot be used.
  3. $+$, $-$, $\times$, $/$,$()$, $\hat{}$ can be used for functions.
  4. You cannot use: round, floor, ceiling, truncate function or functions such as sin, cos, log.
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  • 1
    $\begingroup$ Is sqrt allowed? Also, what about repeating decimal operator? Also, what about decimal points, such as ".3"? $\endgroup$
    – JS1
    Jul 2, 2019 at 23:16
  • 1
    $\begingroup$ Do you mean 67 and 97, or 67 or 97? If you mean or, consider giving @malioboro's answer a checkmark. $\endgroup$
    – Duck
    Jul 2, 2019 at 23:17
  • $\begingroup$ @Duck that answer uses concatenation after modifying the numbers, which is not the same thing as making a multi-digit number out of the original digits. $\endgroup$
    – Bass
    Jul 3, 2019 at 6:34
  • $\begingroup$ Same problem occurred here with my answer: puzzling.stackexchange.com/questions/84834/… $\endgroup$
    – Duck
    Jul 3, 2019 at 15:30

3 Answers 3

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I think this works for 97:

$!(3!)-5!-(3!)!!=97$

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  • $\begingroup$ @Neil W is there any way to combine our answers? $\endgroup$
    – sunfishho
    Jul 4, 2019 at 7:51
  • $\begingroup$ Nice find! For those wondering, this simplifies to $265 - 120 - 48 = 97$ $\endgroup$
    – JS1
    Jul 4, 2019 at 9:03
  • $\begingroup$ I don't even know how lucky I was to find this @JS1 $\endgroup$
    – sunfishho
    Jul 4, 2019 at 15:39
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With a decimal point

$67 = .5^{-(3!)}+3$

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    $\begingroup$ I like this much better than the one with concatenation, because with concatenation it is easy to make both 67 and 97. Example: $5! - ((!3) || 3) = 120 - (2 || 3) = 120 - 23 = 97$ $\endgroup$
    – JS1
    Jul 3, 2019 at 17:08
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( Partial answer)

for 67:

$3! \Vert (!3+5) $

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  • $\begingroup$ Wait, that's not partial, it says 67 or 97, not both. +1 :) $\endgroup$
    – Duck
    Jul 2, 2019 at 22:05
  • $\begingroup$ wait, that is a concatenation, isnt it? is that allowed?? $\endgroup$ Jul 2, 2019 at 23:31
  • $\begingroup$ Doesn't say concatenation isn't allowed. $\endgroup$
    – Duck
    Jul 2, 2019 at 23:36
  • $\begingroup$ @OmegaKrypton I'm not pretty sure, actually. I think the first rule is said that we allowed doing something like concatenation $\endgroup$
    – malioboro
    Jul 3, 2019 at 0:07
  • $\begingroup$ I think that is only applicable for the original numbers? $\endgroup$ Jul 3, 2019 at 0:32

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