Hyellow, Here's a little challenge for all of you... I'm posting a brain puzzle with a double challenge - try to solve it, then post another brain puzzle (or question or test or whatsoever) so the people coming after always have a puzzle to work on and the thread stays alive... And please don't Google for answer, is not a contest to show off who's smarter, but just a way to work out a bit our "brain muscles". So, here's my initial puzzle: Use any mathematical operations between the following numbers to achieve the desired result (any kind of mathematical operations, but only operations, not adding any new numbers in equations). 1 1 1 = 6 2 2 2 = 6 3 3 3 = 6 4 4 4 = 6 5 5 5 = 6 6 6 6 = 6 7 7 7 = 6 8 8 8 = 6 9 9 9 = 6 In the spoiler section I gave three examples of solvings, in case you didn't understood the problem. Still 6 more to be solved. Spoiler 2 + 2 + 2 = 6 3 * 3 - 3 = 6 5 + 5 / 5 = 6

Oh, this is an easy one: Spoiler 111 --> (1+1+1)^log_3[6] = 6 222 --> 2+(2^[2]) = 6 333 --> (3_3)*(3_3)-(3_3) = 6 444 --> (4^[0])+(4^[0])+(4^[1]) = 6 555 --> (5_5)+(5^[0])*(5^[0]) = 6 666 ---> 6 + 6 -6 = f(6) 777 ---> 7 - (7/7) = 6 888 --> 8-(8^[0])-(8^[0]) = 6 999 --> 9 + 9 + 9 != 6 ...or did I misunderstand something...?

Do it without adding any new numbers, just operations. You want to use logarithms, fine, do it, but only applied to existing numbers, not adding new ones. Same for moving numbers to power index or add new numbers for power index. Also all should be equal not "not equal" with 6. And yes, all are definitely possible.

Don't ruin the fun! I was allowed to add operations! Edit: I'll share the proper stuff later or people will click the spoiler and know without trying...