Eryn and Ossie were spinning the spinners shown. If the sum of the numbers from the two spinners was even then Eryn won; if it was odd, then Ossie won.
Now suppose that Eryn and Ossie divided one spinner up into r equal parts and the other into s equal parts. Would the two spinners when spun together be fair or unfair?
Solution
The situation here depends on whether r and s are even.
(i) If at least one of r and s is even, then the spinners are fair.
(ii) If r and s are both odd, then the spinners are unfair.
This is because an even number plus an odd number gives an odd number while two even numbers or two odd numbers gives an even number. If there are an even number of sections on one spinner then for each section on the other spinner (regardless of how many there are) the sum will be even half of the time and odd half of the time.
Extension
Can you make two spinners with r and s sections, respectively, so that the spinners together are unfair?
Can you make two spinners with r and s sections, respectively, so that the spinners together are fair?