Sunday 5 June 2016

mathematics - Use 2 0 1 and 8 to make 67


Use $2$ $0$ $1 $ and $8$ to make the number $67$


RULES




  1. 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





  2. 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.




  3. Sorry, but the integer function may NOT be used. Nor may the round, floor, ceiling, or truncate functions.




  4. +, -, *, /, (), !, 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!



Answer



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 $20!^{(17)}=20\cdot3=60$.



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