Rowland Han of Wydown Middle School was the only winner in the June Math Puzzler contest. Actually, the contest required 12 answers because a couple questions had multiple answers.

For instance, In Question 5, five different possible number combinations were correct.

And, Question 6 needed an answer for each of three different cubes.

Two other kids gave 11 correct answers. But, in Question 5, they included only four of the five possible combinations.

For July, Mr. Math Puzzler has taken into account that school is out. Therefore, next month’s Puzzlers deal with things more suited to vacation time. For instance, there are two questions concerning pizza and one each about card games and spending money.

Mr. Math Puzzler is Wayne Hesse of Green Park Lutheran School in south St. Louis County.

He suggests that competing in the Math Puzzler contest would be a good group activity for the summer. You and your friends could enter the July Math Puzzler competition while enjoying the outdoor weather.

Then, when the August edition comes, you’ll find out how you and your friends did. Maybe, if you get all six Puzzlers correct, you might even win one of the $10 Borders gift certificates that are awarded to winners.

Before trying, however, you ought to check answers to past questions. That way, you can find out how Mr. Math Puzzler’s mind works.

You can do that by clicking on Past Stories on the Home Page. Pick any month from September, 2001, on. Each month, there’s a story that gives the answers to the previous month’s questions.

Answers for June Math Puzzlers

1. What is the speed in miles per hour (rounded to the nearest mph) of a race car that travels the length of a football field (100 yards) in one second?

Answer: 205 mph

The explanation: There are 1,760 yards per mile. If the car goes 100 yards in one second, it would take 17.6 seconds per mile. There are 3,600 seconds per hour, so dividing 3,600 by 17.6 seconds translates into 204.54 miles per hour. Rounding that out brings you to 205 mph.

 

2. Segments AB and CD are diameters of the circle and their lengths are 2 inches each. Find the perimeter of the shaded region (see diagram).

Answer: 7 inches

The explanation: The circumference of a circle is Pi times the diameter. Or, in this case, 6.28 inches. Then, you divide that by 2 since the shaded areas are only half of the total circumference or 3.14 inches. Then, you add 4 inches to take into account the four radius lines that enclose the shaded area to make the perimeter. That’s 7.14 inches, rounded to 7 inches.

 

3. Find the measure of each interior angle of a stop sign.

Answer: 135 degrees

The explanation: There is a formula for figuring the angle of a polygon. That is the number of sides minus 2 times 180 degrees equals the total angle degrees in a polygon. In this case, there are 8 sides. Subtracting 2 leaves 6 and 6 times 180 is 1,080 degrees. Divided by eight angles, that’s 135 degrees each.

 

4. One step is missing from the following directions. (1) Start with your age as an integer, (2) multiply it by 2, (3) then subtract 3, (4) multiply that result by 3. At this point (5), a step is missing. Finally (6) divide by 6 and obtain your age as an answer. What is the missing step?

Answer: adding 9

The explanation: In this formula, “a” is your age. The “plus 9” is the extra step that you need to add to get back to your age.

     3(2a-3)
     -------
        6

 

     6a - 9 (+9)
     -----------
          6

5. What are the possible lengths for the sides of a triangle if the triangle’s perimeter is 13 and the lengths of the sides are integers?

Answer: 1,6,6; 2,5,6; 3,5,5; 3,4,6; 4,4,5

The explanation: The sum of two of the sides has to be greater than the 3rd side, otherwise it wouldn’t be a triangle. That leaves five possible combinations.

 

6. Find the lengths, in feet, of the sides of three cubes. (If using decimals to express your answer, round to the nearest one-hundredth.) Cube A’s surface area equals its volume. Cube B’s surface area equals the square of its volume. For Cube C, square of the surface area equals its volume.

Answer: Cube A: 6 feet
Cube B: 1.57 feet
Cube C: 1/36th feet

The explanation: There are three different formulas to arrive at the three answers. In all the formulas, “a” is the length of the edge of the cube.

Cube A formula:

6a² = a³

6a² = a * a²

a = 6

 

Cube B formula:

 

Cube C formula:

(6a²)² = a³

36a⁴ = a³

36a * a³ = a³

36a/36 = 1/36

a = 1/36