Use digits 3 3 5 to make 67 or 97

Question

Rules:

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. $33$).
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.
$+$, $-$, $\times$, $/$,$()$, $\hat{}$ can be used for functions.
You cannot use: round, floor, ceiling, truncate function or functions such as sin, cos, log.

Is sqrt allowed? Also, what about repeating decimal operator? Also, what about decimal points, such as ".3"? — JS1, Jul 02 '19 at 23:16
Do you mean 67 and 97, or 67 or 97? If you mean or, consider giving @malioboro's answer a checkmark. — Duck, Jul 02 '19 at 23:17
@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. — Bass, Jul 03 '19 at 06:34
Same problem occurred here with my answer: https://puzzling.stackexchange.com/questions/84834/use-1-9-6-2-in-this-order-to-make-75 — Duck, Jul 03 '19 at 15:30

score 9 · Answer 1 · edited Jul 03 '19 at 19:20

9

With a decimal point

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

edited Jul 03 '19 at 19:20

Weather Vane

answered Jul 03 '19 at 14:04

Neil W

2

I like this much better than the one with concatenation, because with concatenation it is easy to make both 67 and 97. Example: $5! - ((!3) || 3) = 120 - (2 || 3) = 120 - 23 = 97$ – JS1 Jul 03 '19 at 17:08

score 7 · Accepted Answer · answered Jul 04 '19 at 07:50

7

I think this works for 97:

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

answered Jul 04 '19 at 07:50

sunfishho

@Neil W is there any way to combine our answers? – sunfishho Jul 04 '19 at 07:51
Nice find! For those wondering, this simplifies to $265 - 120 - 48 = 97$ – JS1 Jul 04 '19 at 09:03
I don't even know how lucky I was to find this @JS1 – sunfishho Jul 04 '19 at 15:39

score 4 · Answer 3 · answered Jul 02 '19 at 21:52

4

( Partial answer)

for 67:

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

answered Jul 02 '19 at 21:52

malioboro

Wait, that's not partial, it says 67 or 97, not both. +1 :) – Duck Jul 02 '19 at 22:05
wait, that is a concatenation, isnt it? is that allowed?? – Omega Krypton Jul 02 '19 at 23:31
Doesn't say concatenation isn't allowed. – Duck Jul 02 '19 at 23:36
@OmegaKrypton I'm not pretty sure, actually. I think the first rule is said that we allowed doing something like concatenation – malioboro Jul 03 '19 at 00:07
I think that is only applicable for the original numbers? – Omega Krypton Jul 03 '19 at 00:32
Yes, I have answered these types before (by @ThomasL) and that is what it usually means. – Duck Jul 03 '19 at 01:06
sorry, I was not clear about the concatenation. I just had in mind 33, 35, 53, so I would prefer a solution without a concatenation, where a digit is manipulated, but great findings! – ThomasL Jul 03 '19 at 21:09

3 Answers3