In the picture above, all the numbers 1-12 are given, using only three nines. Now, I want to make a similar watch, but using fours instead of nines.
Can you make a list of the numbers 1-12 using exactly three fours (for each number). So, for instance, you can't do 4+4 to get 8.
A few rules:
- Combining two 4s to make 44 is not legal
- Repeating / recurring decimal representation is not legal (as used to get seven in the example watch).
- Flooring / rounding is not legal
- The answer must be exact.
- Parentheses are of course OK
You are free to use other functions, but it's possible to do this using only elementary functions and the factorial !
(no other "Special functions" (as they are called in the wiki-article)).