Three get April Puzzlers; all win certificates

In March, the three Math Puzzler winners who received Borders book certificate prizes needed both skill and some luck. But, this month, the same three won again but needed only skill this time.

In March, Clayton Vance, Phillip Hsu and Drew Fender were among 10 entrants who answered all six Math Puzzler questions correctly. Since Young Saint Louis.com awards only three certificates, the three had to survive a random drawing.

But, this month, the same three answered the April Math Puzzler questions correctly. But, this time, they were the only entrants who got all answers right so all three again receive the book certificate prizes..

YSL.com congratulates Clayton, Phillip and Drew for getting the answers correct for the second month in a row. Their $10 Borders certificates were put in the mail May 1.

The three double-winners are all from different schools. Clayton is from Mason Ridge Elementary, Phillip is from Wild Horse Elementary and Drew is from Sperreng Middle School.

We also want to remind kids who enter the Math Puzzler competition to make sure they get their entries mailed early. In April, we got Puzzler mail that was postmarked after the 15th of the month so their entries couldn't be counted.

If you are a first-time entrant in the Math Puzzler competition, you might like to do some reviewing of past questions and answers. That way, you'll get a chance to understand the thinking of Mr. Math Puzzler, Mr. Wayne Hesse. He's a mathematics teacher at Green Park Lutheran School in South St. Louis.

He started writing Puzzlers for YSL.com in September, 2001. Therefore, you can use the Past Stories tab on the home page to find past issues. Just pick a month after the 2001 start and read the questions. Then, click on the next month to find the answers. Each Puzzler answer includes an explanation.

(To find the May Puzzler questions and contest entry form, click here.)

The Answers to April Math Puzzlers:

1. Sue and Jim were practicing free throws and each made 75 out of 100. After a little break, Jim tried again and hit 37 out of 50 shots. Sue did not do any more shooting. Who had the better percentage for the day?

Answer: Sue, with 75%

Explanation: Both shot 75% in the first round of 100 shots. But, Jim's second round left him with 112 of 150. That was just short of 75%; 74.67% to be exact.

 

2. A solid white cube that measures four inches on all sides is painted black on all six faces. The cube is then cut up into smaller cubes measuring one inch on all sides. Some of the smaller cubes have three black faces, some will have two, some will have one and some are completely white. How many of each kind of smaller cube will there be?

Answer: 8 three-sided; 24 two-sided;
24 one-sided and 8 all white.

Explanation: This is one of those Math Puzzlers where a good three-dimensional diagram and some visualization will bring you the right answer.

 

3. A bull frog and a green frog have a race from a starting line to a point 12 feet away and back to the starting line. Both frogs travel at the same rate of one foot in four seconds. However, the bull frog can jump in only 10-inch leaps and the green frog can jump only in 6-inch leaps. Which frog wins the race and by how much?

Answer: Green frog by 4 seconds

Explanation: The difference here is that the bull frog's 10-inch leaps take him past the finish line. That means he needed 15 leaps to complete the circuit when 14.4 leaps were all that were needed. Each of his jumps took 3 1/3 seconds for a total 100 seconds. The green frog's 12 leaps got him right to the finish line and another 12 back for a total of 24 leaps. Each of his jumps took 2 seconds, for a total of 96 seconds. That's 4 seconds less because bull frog ended up jumping one foot further.

 

4. You have two candles, one of which is eight inches tall and can burn for four hours before it is all gone. The other is shorter and fatter. It is six inches tall and can burn for five hours. If both candles are lit at the same time, how long will they have to burn until both have the same length?

Answer: 2.5 hours

Explanation: The taller candle burns at 2 inches per hour. The shorter one burns at 1 1/5 inches per hour. You can convert that into the following formula:

      8 - 2h = 6 - 6/5h
         +2h        +2h
     -------   --------
      8      = 6 + 4/5h
     -6       -6
     -------  ---------
      2      =     4/5h

 

     5/4 (2) = (4/5h) 5/4

        10/4 = h

                       2.5 = h

 

5. How can you make four equilateral triangles by using six toothpicks? (This answer can be an illustration or a word description.)

Answer: A triangle pyramid

Explanation: By making a three-dimensional pyramid, you can have four equilateral triangles on the three sides and bottom of the pyramid and only use six toothpicks.

 

6. Suppose a typical license plate is composed of three letters followed by three numbers. How many license plates can be made if no letters or numbers can be duplicated on the same plate?

Answer: 11,232,000

Explanation: This is a probability problem. There are 26 letters in the alphabet so that involves multiplying 26 chances for the first letter, 25 for the second and 24 for the third. There are 10 chances for the first number, 9 for the second and 8 for the third. That formula is:

26 x 25 x 24 x 10 x 9 x 8 = 11,232,000