Here are my six solutions. flagamuffin found one of them - kudos! 15 = (1 x 5)!! 24 = (2+√4)! 24 = (√ ( 2 x 4!! ) )! (I'm pretty proud of that one!) 36 = 3 x 6! 46 = -√4 + 6!! 48 = ( (4! / 8)! ) !! (another tricky one!) Four of my solutions make use of double factorial. 4!! = 8 and 6!! = 48. I've worked on this on and off for a few days while I've been traveling -- a great airplane puzzle. And I've worked out a lot of strategies and smart ways to think about solutions. Key is not starting with a number and trying to make a solution, but to look at what operations are available and which ones will get near to the result you want. By the way, if you don't like the double factorial (I hear sometimes from people that think it's cheating), it is a real function and I solved a problem some years ago dealing with probability that made use of this function, although I didn't know the function at the time.
It's not cheating, but I still don't like the double factorial. I had an inkling a lot of the other solutions made use of it, and since it's not something those of us who finished formal math for good by the age of 19 internalized, it's much harder to use in solutions that require intuitive leaps. Nonetheless, best use of the quiz tag in a long time!!
I like your double exclamation point at the end of your comment!! I'll argue it's not harder to use in solutions -- I gave an explanation in the puzzle to open up the possibility, and it's a pretty short list of operands that are useful: 4!! = 8 5!! = 15 6!! = 48 7!! = 105 after that, the numbers get too big to be useful. I didn't find a use for 5!! or 7!!, but certainly there are more solutions I haven't found!