math riddle

Welcome to A2K crazy mad0.

You just lost your bet. What were you betting?
The number on the bottom slice is 84.

Explaination required for the simple-minded (ie me).

there appears to be a "opposite slice (* or / 3) [(+ or -)1" thingy going on here - except for the missing slice that is.

Is that it?

Yes.

And I didn't explain it so that others could still try to solve it.
There is a relation between the opposite slices only. The smallest number is one third the size of the biggest (rounded to the closest whole number). That leaves two possible numbers for the empty slice you might think, "756" and "84". There is certain symmetry, indicating that "84" is correct. It bothers me slightly that there are 4 opposite slices, because "89" and "268" might as well have switched places. 10 slices would have been completely symmetrical and made this thing better in my opinion.

84 is wrong. What relation leads to 84?

Well I wrote how i came up with 84 in the post above. And when I went over it again, I see that something is not right.

Here are the relations:
(268-1)/89=3
(934-1)/311=3
(520-1)/173=3

This works with all the numbers and can't possibly be a coincidence. But this would not lead to a whole number in the questioned sice. IF we are to divide with three in the same direction as all the other numbers. So it would make more sense perhaps that 757 is the right number.
(757-1)/252=3

I also have a theory of why the direction of the dividing of the opposite slices seem to go in random directions. If you imagine or draw the "pizza" with the numbers you will see it more clearly. I think you are just supposed to either divide or multiply to get your whole number. This way any other slice could have been a question mark, and there would only be one solution. Example: (311-1)/3= 103,666.. so it must be 311*3+1=935

Can any body put up the 8 slices with the numbers in code since I do not understand how it looks like.


Whim

Looks like this:

-----------------------------252
--------------------934-------------520

------------------268-------------------89

-------------------- 173------------311
------------------------------?

Aha. Thanks.