OK so it's 5775 according to the Hebrew calendar. Which means of course that it's Problem of the year time (well ok it's a bit late but so what).

5775 turns out to be kinda tough (or I'm being silly).

(5+7)/(7+5)=1 is pretty easy.

getting 5-sqrt(7+7-5)=2 took me quite a while.

I have at the time of writing no way to get 3.

5-(7/7)^5=4

5*((7/7)^5)=5

5+(7/7)^5=6

all sort of fit together.

7 like 3 I don't have yet, although I've spent less time on it.

5+sqrt(7+7-5)=8

5-(7/7)+5=9

5*(7/7)+5=10

5+(7/7)+5=11

again fit into a nice group.

This is about where I stopped thinking about these (because 3 and 7 where incomplete).

So naturally the point of this post is to see what people come up with for the 3,7 and things bigger than 11. Enjoy!

If you're allowed an initial minus then

ReplyDeletesqrt((-5 + 7) * 7 - 5) = 3

5 + sqrt(7*7) - 5 = 7

sqrt((5+7)*(7+5)) = 12

5 + 7 + 7 - 5 = 14

5 * sqrt(7 + 7 - 5) = 15

sqrt(5! + (7/7)) + 5 = 16