Using only addition, how do you add eight 8’s and get the number 1000?

Question

anonymous · Answer

+8 
+8 
+8 
+88 
+888

kainui · Answer

I think the way to figure this out is to realize that if you add up 8's you need to have the one's place be 0. So that might give you an idea of how many different numbers you have to add up.

8=8
8+8=16
8+8+8=24
8+8+8+8=32
8+8+8+8+8=40

So this tells us that we need 5 numbers to get it to end in 0.

kainui · Answer

From there, the other three 8's we're left will have to go in front of these 5 numbers. That's not too bad to just sort of look through all the possibilities to see what works.

8+8+8+8+8888
8+8+8+88+888
8+8+88+88+88

Those are the only 3 different ways to arrange the 8's.

Obviously 8888 is over 1000, so that's wrong. And obviously 3 88's and 2 8's is too low. So we're left with this which has to be it without even calculating much of anything!

tanya123 · Answer

Cool, thanks for the explanation!!

kainui · Answer

Yeah, that was a fun one, do you have any more like this? XD