MathDB

14

Part of 2014 ASDAN Math Tournament

Problems(2)

2014 General #14

Source:

7/5/2022
Patricia has a rectangular painting that she wishes to frame. The frame must also be rectangular and will extend 3 cm3\text{ cm} outward from each of the four sides of the painting. When the painting is framed, the area of the frame not covered by the painting is 108 cm2108\text{ cm}^2. What is the perimeter of the painting alone (without the frame)?
2014General Test
2014 Team #14

Source:

7/1/2022
Consider a round table on which 20142014 people are seated. Suppose that the person at the head of the table receives a giant plate containing all the food for supper. He then serves himself and passes the plate either right or left with equal probability. Each person, upon receiving the plate, will serve himself if necessary and similarly pass the plate either left or right with equal probability. Compute the probability that you are served last if you are seated 22 seats away from the person at the head of the table.
2014team test