How do you find the average of two numbers if you're not allowed to add the two numbers together or divide more than once?

Question

anonymous · Answer

Just find the middle value...

solomonzelman · Answer

draw a number line, and start walking from the 2 numbers (with the same speed) towards each other, and see where they meet at ;)

anonymous · Answer

If you have 68 and 74, find the number which is equidistant from 68 as well as 74..

solomonzelman · Answer

Find the half of the difference between the 2 numbers, and add it to the lesser number, or subtract it from the bigger number.

kainui · Answer

For this riddle I'm asking, I'm looking for an algebraic statement given x and y.

solomonzelman · Answer

(number 1  -  number 2 ) ÷ 2 = difference

And then add to a smaller num. or subtract from a bigger num.

idk...

solomonzelman · Answer

I didn't do anything invalid, did  I ?

solomonzelman · Answer

Caling numb 1 - the biggest, and number 2 - the smallest

kainui · Answer

Also I suppose I should say that you're not allowed to know if x or y is larger than the other.

The reason this comes up is I was playing around with the binary search algorithm and realized that you have to find the average of two numbers many times.

So if your values x and y are too large, adding them gives you an overflow error. And dividing is something I'd like to cut down on to save time haha.

solomonzelman · Answer

│ x-y│ ÷ 2   is the difference

kainui · Answer

I don't think it should matter though if you're finding the average.

solomonzelman · Answer

I meant half of difference, but perhaps you are right, because we can't add, since the largest and smallest numbers aren't known.

kainui · Answer

You're pretty much right, I guess I'll just say it:

$$\LARGE \frac{x+y}{2}=x+\frac{y-x}{2}$$

solomonzelman · Answer

x+y   on the first numerator. You can not do this !

solomonzelman · Answer

You said you can't add the numbers together

solomonzelman · Answer

:)

kainui · Answer

No I'm showing that the left is what we want is equivalent to the thing on the right which does not violate the rules.

solomonzelman · Answer

oh,  like that... I sort of see.

solomonzelman · Answer

you solved it

x+ (y-x)/2

I didn't know how to express this , but I thought of it

kainui · Answer

Yeah it has to be something a computer can evaluate lol. Thanks for playing! =P

solomonzelman · Answer

Yeah, good game :)