Friday, July 31, 2009

July 31, 2009

A line passes through A(1, 1) and B(100, 1000). How many other points with integer coordinates are on the line and strictly between A and B?

Interactive version of problem and solution.



Thursday, July 30, 2009

July 30, 2009

You have nine coins: a collection of pennies, nickels, dimes, and quarters having a total value of $1.02, with at least one coin of each type. How many dimes must you have?

Interactive version of problem and solution.



Wednesday, July 29, 2009

July 29, 2009

A circle passes through the three vertices of an isosceles triangle that has two sides of length 3 and a base of length 2. What is the area of this circle?

Interactive version of problem and solution.

Buy The Contest Problem Book VI

Tuesday, July 28, 2009

July 28, 2009

Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers 1 through 10. Each throw hits the target in a region with a different value. The scores are: Alice 16 points, Ben 4 points, Cindy 7 points, Dave 11 points, and Ellen 17 points. Who hits the region worth 6 points?


Monday, July 27, 2009

July 27, 2009

Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by 10%. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost $40 on Thursday?

Interactive version of problem and solution.

Buy Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi from the MAA Bookstore

Friday, July 24, 2009

July 24, 2009

On a certain math exam, 10% of the students got 70 points, 25% got 80 points, 20% got 85 points, 15% got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam?


Thursday, July 23, 2009

July 23, 2009

Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. How many elements are common to S and T?

Interactive version of problem and solution.




Buy The Contest Problem Book IX

Wednesday, July 22, 2009

July 22, 2009

A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by 25% without altering the volume, by what percent must the height be decreased?

Interactive version of problem and solution.


Tuesday, July 21, 2009

July 21, 2009

A collector orders to buy state quarters for 2000% of their face value. At that rate how much will Bryden get for his four state quarters?

Interactive version of problem and solution.


Thursday, July 16, 2009

July 16, 2009

Antonette gets 70% on a 10-problem test, 80% on a 20-problem test and 90% on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?

Interactive version of problem and solution.

Buy The Contest Problem Book VI

Wednesday, July 15, 2009

July 15, 2009

The digits 1, 2, 3, 4, 5, 6, 7, and 9 are used to form four two-digit prime numbers, with each digit used exactly once. What is the sum of these four primes?


Tuesday, July 14, 2009

July 14, 2008

Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?

Interactive version of problem and solution.

Buy Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi from the MAA Bookstore

Monday, July 13, 2009

July 13, 2009

Carlos Montado was born on Saturday, November 9, 2002. On what day of the week will Carlos be 706 days old?


Wednesday, July 8, 2009

July 8, 2009

Riders on a Ferris wheel travel in a circle in a vertical plane. A particular wheel has radius 20 feet and revolves at the constant rate of one revolution per minute. How many seconds does it take a rider to travel from the bottom of the wheel to a point 10 vertical feet above the bottom?

Interactive version of problem and solution.


Tuesday, July 7, 2009

Monday, July 6, 2009

July 6, 2009

An athlete's target heart rate, in beats per minute, is 80% of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from 220. To the nearest whole number, what is the target heart rate of an athlete who is 26 years old?


Thursday, July 2, 2009

July 2, 2009

How many non-empty subsets S of {1, 2, 3, . . . , 15} have the following two properties?

(1) No two consecutive integers belong to S.

(2) If S contains k elements, then S contains no number less than k.

Interactive version of problem and solution.

Buy Hexaflexagons, Probability, Paradoxes, and the Tower of Hanoi from the MAA Bookstore

Wednesday, July 1, 2009

July 1, 2009

Call a number "prime-looking" if it is composite but not divisible by 2,3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many prime-looking numbers are there less than 1000?