306
just some dice I threw around. nothing to see here
(lemmy.blahaj.zone)
Alt text: Five dices. Top left corner is a three, top right corner is a six, bottom left corner is also a six and bottom right corner is two threes forming a straight angle.
If you allow factorials:
6^3 - 6! / (3! * 3!) = 196
Edit: also 66*3 - 3!/3 = 196
Factorials or something more than basic arithmetic (+exponents) is needed as I went ahead and programmatically checked every expression without parenthesis and the closest would always be 195. Interestingly, all values within a difference of 10 were multiples of 3.
A lost cause indeed.
If we allow combining digits to make larger numbers (like kittehx's edit) we can actually do
(33*6) - (6/3) = 196
How did I not try that? Now I feel dumb lol
If it's limited to basic arithmetic (+-*/) and no parenthesis, would there be any answer possible that's not a multiple of 3? My first thought is telling me that common order of operations would make any equation using the numbers in the OP and the restrictions laid out would always amount to a multiple of 3.
That was my initial thought, but you can do add or sub by 2 (6 / 3) to get a non-multiple of 3. I had to double check and see that there were in fact values of i.e. x.5 within I think a difference of 64, can’t remember the exact values or their expressions.
Oh yep, my bad. It's always division that throws me in math expressions that have multiple steps to them.