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POTW #24

2008-04-16T09:12:00.000-07:00

A basketball coach wants to hang three plaques. The wall is 9 feet high and 11 feet wide. She wants to hang the three plaques side by side so that the group of plaques is centered horizontally with 6 inches of space between plaques, with the center of each plaque 5 feet from the floor. If each plaque is 14 inches tall and 20 inches wide, where should she place the top-left corner of the left-most plaque? (hint...Drawing a picture may help you solve this problem.)

PROBLEM OF THE WEEK #22

2008-03-03T06:35:00.001-08:00

An isosceles right triangle with legs of length 16 is partitioned into 16 congruent triangles, as shown. The area of the shaded region is ___ square units.

PROBLEM OF THE WEEK #20

2008-02-11T09:00:00.000-08:00

Write the following expression as a simple fraction in lowest terms.

Problem of the Week #18

2008-01-23T05:41:00.000-08:00

Smith, Robinson, and Jones are a conductor, a porter, and an engineer on a certain train. Also aboard the train are three passengers with the same last names: Mr. Smith, Mr. Robinson, and Mr. Jones.

Mr. Robinson lives in Detroit.

The porter lives exactly halfway between Chicago and Detroit.

Mr. Jones earns exactly $50,000 per year.

The porter’s nearest neighbor, who is one of the three passengers, earns exactly three times as much as the porter.

Smith usually beats the conductor at tennis.

The passenger whose last name is the same as the porter’s lives in Chicago.

Who is the engineer?

PROBLEM OF THE WEEK #16

2008-01-09T05:49:00.000-08:00

The following information was obtained by studying the orders of the people who dined in a certain restaurant one evening.

50 people ordered soup.

65 people ordered dessert.

20 people ordered soup and dessert.

15 people ordered salad and soup.

30 people ordered salad and dessert.

8 people ordered salad, soup, and dessert.

12 people ordered neither salad, soup, nor dessert.

How many people ordered salad and dessert but not soup?

How many people were there in all?

PROBLEM OF THE WEEK #14

2007-12-05T07:14:00.001-08:00

PROBLEM OF THE WEEK #12

2007-11-14T10:25:00.000-08:00

What is the ones digit of 8²⁰⁰⁷ ?

PROBLEM OF THE WEEK #10

2007-10-30T09:01:00.000-07:00

2007-10-16T08:55:00.000-07:00

PROBLEM OF THE WEEK #8

Three apples and two pears cost 78¢. But two apples and three pears cost 82¢. What is the total cost of one apple and one pear?

Problem of the Week #6

2007-10-01T04:47:00.000-07:00

Andy was on his way to a marble tournament when he met Bob. Andy’s bag of marbles was heavy, so he gave Bob one-half of his marbles plus 2. Then he met Alex and gave him one-fourth of his remaining marbles plus 5. Just before arriving at the tournament, he met Emily and gave her one-half of the marbles he had left. When he got to the tournament, he had 2 marbles left. How many marbles did he start with?

Problem of the Week #4

2007-09-11T11:02:00.001-07:00

Suppose that you roll two triangular pyramids, each of which has faces numbered from 1 through 4. What are your chances of rolling a sum of 5?

Problem of the Week #2

2007-08-29T05:56:00.000-07:00

If 40♦ represents a three-digit positive integer with a ones digit of ♦ and 1♦ is a two-digit positive integer with a ones digit of ♦,what value of ♦ makes the equation

40♦ ÷ 27 = 1♦ true?