Problems of the Week--1/9/09

MathCounts Inspired Problems
Double points week! Answers due Friday by noon.

1. February 2 was Groundhog Day. Every February 2, Punxsutawney Phil lumbers out of his home to predict the end of winter by looking for his shadow. If Phil sees his shadow, legend says that we will have 6 more weeks of winter. If the groundhog does NOT see his shadow we will have an early spring.

2. According to the “official” Groundhog Day website, Punxsutawney Phil is 123 years old. Normally, groundhogs live up to 6 years in the wild. If Phil is 123 years, by what percent has he exceeded the normal, unaided lifespan of his species?

3. A groundhog is also known as a woodchuck. Diana writes the letters w, o, o, d, c, h, u, c and k on separate pieces of paper and places the pieces of paper in a bag. If Diana randomly draws one piece of paper from the bag, what it the probability that the letter drawn is also contained in the word groundhog? Express your answer as a common fraction.

4. Groundhog Greg’s burrow has 5 holes he can enter or exit through. If he never exits through the same hole he entered through, how many entrance/exit combinations can Greg choose from? Note that entering through A and leaving through B is not the same as entering through B and leaving through A.

5. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...

6. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...

7. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...

8. A worm has to climb a barrier 19 feet high. It climbs 8 feet every day and slips down 5 feet every night. Starting from the bottom of the barrier on Sunday morning, on which day of the week will the worm reach the top of the barrier?

9. How many fifteen-minute appointments can a doctor fit into her schedule if she works from 8:30 am to noon and from 1 pm to 4:30 pm?

10. On a $12.00 purchase, Michael was offered 3 successive discounts of 25%, 20% and 10% each in any order he wished. What is the difference in dollars between applying the discounts in order from greatest to least and in order from least to greatest?