It is Pi Day on Friday, March 14th (3.14)!

Mom baked a delicious raspberry pie.

Dad enjoyed a standard-size piece (1/6 of a pie).

Youngest son had one, too, and snuck another 1/2 piece.

Middle son did the same.

Oldest son had the average amount of pie among the four.

This left a small piece for Mom. The family kitten got into it and smeared half of that all over the kitchen counter.

How much of the pie got smeared?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, March 26, 2014 at noon Pacific Time.** I will post the answer shortly after.