Use 2 0 1 and 8 to make 67

Question

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!

@user477343 also $8^2 + 0 + 1 = 65$, $80-12=68$, $8^2 + (1 \times 0) = 64$, $8^2 - 0 - 1 = 63$, and $8^2 - 0! - 1 = 62$ haha!! — El-Guest, Sep 09 '18 at 00:59
@Vicky it atcually makes swnse to disallow square. It would make the puzzle almost trivial. — Marius, Sep 09 '18 at 14:33
@Marius, the stated reason to exclude square is because that would use the 2 (ie if you do want to square you have to do 8^2 and that counts as using the 2) and for consistency the same should apply to sqrt - if you want to use sqrt you should do 8^(1/2). — Vicky, Sep 09 '18 at 18:19
$\sqrt{x}$ The 2 is implied, but I don't actually have to write it on the page. That's why sqrt is generally allowed in these types of puzzles. — nickgard, Sep 09 '18 at 19:19
67 because it is the hardest number to get. Try 88, or 57. Easy, right? — Alto, Sep 09 '18 at 19:35

JMP · Accepted Answer · 2018-09-08T23:14:21.273

14

How about:

$(8!!!!+1)\times2+0!\\=(8\cdot4+1)\times2+1\\=(32+1)\times2+1\\=33\times2+1\\=66+1\\=67$

and similarly, with the digits in order:

$20!!!!!!!!!!!!!!!!! - 1 + 8$, where $20!^{(17)}=20\cdot3=60$.

edited Sep 08 '18 at 23:14

answered Sep 08 '18 at 22:27

JMP

35,612
7
78
151

4

I think $8!! = 8 \times 6 \times 4 \times 2$ – El-Guest Sep 08 '18 at 22:28
3

@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 – El-Guest Sep 08 '18 at 22:33
4

8!!!! is a multi-factorial – JMP Sep 08 '18 at 22:33

score 12 · Answer 2 · answered Sep 09 '18 at 04:37

12

$$8^2 + \sqrt{\frac{0!}{.\bar{1}}} = 64 + \sqrt{\frac{1}{\frac{1}{9}}} = 64 + 3 = 67$$ Not that $.\bar{1}$ is 0.111111... recurring.

answered Sep 09 '18 at 04:37

Ian Miller

460
2
11

1

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 – Mr Pie Sep 09 '18 at 05:21
1

Nice answer! Welcome to Puzzling. – Vicky Sep 09 '18 at 08:06

score 10 · Answer 3 · answered Sep 08 '18 at 22:40

10

$8!!! - 12 - 0! = 8 \times 5 \times 2 - 12 - 1 = 80-13 = 67$

answered Sep 08 '18 at 22:40

Marius

18,049
4
54
101

1

that is brilliant, but is your function after the 8 allowed??? – tom Sep 08 '18 at 22:41
don't know. I guess we'll find out – Marius Sep 08 '18 at 22:42
plus one and we will see :-) didn't know that was possible... – tom Sep 08 '18 at 22:42

score 2 · Answer 4 · answered Sep 09 '18 at 18:02

2

I base my answer on

75 (20 minus 18 in base 75 is 67 when converted back to decimal.)

answered Sep 09 '18 at 18:02

CyberianRat

367
1
6

score 1 · Answer 5 · answered Sep 10 '18 at 07:49

1

(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

answered Sep 10 '18 at 07:49

holydragon

300
1
4

Arc · Answer 6 · 2018-09-09T14:18:01.307

0

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.

edited Sep 09 '18 at 14:18

answered Sep 09 '18 at 13:20

Arc

121
3

1

Please make use of the spoiler tag >! – ə̷̶̸͇̘̜́̍͗̂̄︣͟ Sep 09 '18 at 13:37
1

Added spoiler tag. – Arc Sep 09 '18 at 14:19
1

Why the downvotes? – Arc Sep 09 '18 at 21:25
I did not downvote. – ə̷̶̸͇̘̜́̍͗̂̄︣͟ Sep 10 '18 at 06:19
+1 Why downvote?? – Sep 10 '18 at 08:39

Use 2 0 1 and 8 to make 67

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