[tab]Yes, I was suggesting that you use the square root, since it can be denoted by √ which does not require using a number. Contrast this with other roots such as the cubed root that requires using the number “3” however you present it. The square root may also be represented by raising a quantity to the power “1/2”, which involves using a number, but using the √ symbol remains within the designated rules. The ! symbol to denote “factorial” is fine for the same reason, even if its expansion would involve adding other numbers.
Perhaps I didn’t explain that rule sufficiently.
Also, only the integers provided at the beginning of the problem are the only ones allowed - so no “x root of c + c + c, where x is whatever irrational number root results in 6” or “log base y where y is a number that when raised to the 6th power equals c + c + c”. And no use-defined operators either! Lol. Only conventional mathematical ones - I should have been more explicit on that one too Nice idea though. I’ve enjoyed all of your contributions to this problem, even though some of them did not fall inside the rules I was trying to communicate.
( 9/sqrt(9) ) +sqrt(9) = 6 and 8 - sqrt( sqrt( 8+8 ) = 6 are both lovely.
I would even say they’re better than the solutions I was expecting, which were:
(√9 x √9) - √9 = 6 and (√(8/8 + 8 ))! = 6
Though I do prefer √4 + √4 + √4 = 6 for the 4s.[/tab]
So Carleas has solved them all =D>
A shame nobody else contributed.
EDIT:
I got distracted writing this reply, as usual, so by the time I previewed it there were more contributions.
JSS, that’s correct.
FJ:
[tab]By that argument, all conventional mathematical operators would involve extra numbers if fully expanded. My bad for not explicitly stating exclusively conventional mathematical operators in the rules. Carleas has already experimented with user-defined operators in much the same way as you suggest, though maybe you resisted opening the tabs which show this.
Not to say both of your arguments are invalid - they’re good points. I just didn’t mean to imply that you could use them when I described the problem. Both square roots and factorials were supposed to be fine, along with addition, subtraction, multiplication and division. No numbers have to be used when using certain conventional mathematical operators for each of these.[/tab]