Use 2 0 1 and 8 to make 67
Use 2 0 1 and 8 to make 67
Use $2$ $0$ $1 $ and $8$ to make the number $67$
RULES
You must use all 4 digits.
Only the digits 2, 0, 1, and 8 can be used.
You can make multi-digit numbers out of the numbers. Examples: 20, 82, 2.8
The square function may NOT be used. Nor may the cube, raise to a fourth power, or any other function that raises a number to a specific power.
You may use the ^ operation if you use a digit, for example, [(8 + 1)^2 - 0!] is acceptable (if you're trying to get 80), because 2, 0, 1, and 8 is used.
However, [20 ^ 2 / 8 + 1] can't be used to get 51 because it uses an extra 2.
Sorry, but the integer function may NOT be used. Nor may the round, floor, ceiling, or truncate functions.
+, -, *, /, (), !, sqrt, ^, and !! may be used for functions.
Please no brute-force methods. Good luck.
I see that there are many answers. I like #3 because it doesn't use more than 2 factorials, but the most upvoted one gets the credit.
Wow! You guys are good!
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You have my Up-Vote :D
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– QuantumTwinkie
Sep 8 '18 at 21:49
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$8^2+0!+1=66$ dammit!
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– user477343
Sep 9 '18 at 0:12
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Fun fact! $frac8!20+1=2017$
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– Bennett Bernardoni
Sep 9 '18 at 2:14
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Out of curiosity, why 67?
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– user1717828
Sep 9 '18 at 3:47
6 Answers
6
How about:
$(8!!!!+1)times2+0!\=(8cdot4+1)times2+1\=(32+1)times2+1\=33times2+1\=66+1\=67$
and similarly, with the digits in order:
$20!!!!!!!!!!!!!!!!! - 1 + 8$, where $20!^(17)=20cdot3=60$.
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I think $8!! = 8 times 6 times 4 times 2$
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– El-Guest
Sep 8 '18 at 22:28
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@Marius I think this is correct based on the definition of the quadruple factorial; it’s up to OP to decide whether the quadruple factorial is allowed as a valid operation for this puzzle. Great answer though, JonMark Perry!! Love it! :D
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– El-Guest
Sep 8 '18 at 22:33
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8!!!! is a multi-factorial
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– JonMark Perry
Sep 8 '18 at 22:33
$$8^2 + sqrtfrac0!.bar1 = 64 + sqrtfrac1frac19 = 64 + 3 = 67$$
Not that $.bar1$ is 0.111111... recurring.
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Hello! Welcome to the Puzzling Stack Exchange (Puzzling.SE) and great answer, too! I see that you are familiar with the Stack Exchange community since you have been given the $+100$ reputation bonus (and correct me if I'm wrong, but have I seen you on Math.SE?); though I still suggest you visit the Help Center for more information (particularly here then here in the Asking section as you have not asked a question yet). Happy Puzzling! :D
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– user477343
Sep 9 '18 at 5:21
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Nice answer! Welcome to Puzzling.
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– Vicky
Sep 9 '18 at 8:06
$8!!! - 12 - 0! = 8 times 5 times 2 - 12 - 1 = 80-13 = 67$
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that is brilliant, but is your function after the 8 allowed???
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– tom
Sep 8 '18 at 22:41
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don't know. I guess we'll find out
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– Marius
Sep 8 '18 at 22:42
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plus one and we will see :-) didn't know that was possible...
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– tom
Sep 8 '18 at 22:42
I base my answer on
75 (20 minus 18 in base 75 is 67 when converted back to decimal.)
How about 2, 0 + 1, 8. If 2, 0 is in base 16 and 1, 8 is in base 27, it adds to 67 in base 10.
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Please make use of the spoiler tag >!
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– TheSimpliFire
Sep 9 '18 at 13:37
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Added spoiler tag.
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– Arc
Sep 9 '18 at 14:19
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Why the downvotes?
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– Arc
Sep 9 '18 at 21:25
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I did not downvote.
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– TheSimpliFire
Sep 10 '18 at 6:19
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+1 Why downvote??
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– Holyprogrammer
Sep 10 '18 at 8:39
(2+1)! [connects (multi-digit) with] 8-0!
3! [connects (multi-digit) with] 8-1
3*2 [connects (multi-digit) with] 7
6 [connects (multi-digit) with] 7
67
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Solve with 2017 or 2018?
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– Dude_Scott
Sep 8 '18 at 21:42