Math CentralQuandaries & Queries


Question from Allison, a student:

All wiffs are miffs. all miffs are kiffs. There are 25 wiffs. There are 76 kiffs. 33 kiffs are not miffs. How many miffs are not wiffs?


Hi Allison,

Using a piece of chalk I would draw a circle on the gym floor and have the 25 wiffs sit on the floor inside the circle. Now draw a second circle for the miffs to sit in. Since all the wiffs are also miffs the miff circle must be large enough to include surround the wiiff circle.

wiffs and miffs

Now draw a circle for the kiffs. Since all the miffs are kiffs the kiff circle must be large enough to surround the miff circle.

wiffs, miffs and kiffs

There are 76 kiffs to seat inside the kiff circle. The 25 wiffs already seated are also kiffs so there are 76 - 25 = 51 kiffs remaining to be seated. There are 33 kiffs who are not miffs. Where do you seat them? Once you have done so there are 76 - 25 - 33 = 18 remaining to be seated. Where do you seat them?

I hope this helps,

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