There were three winners in the December Math Puzzler competition. That broke a string of two straight months when Mr. Math Puzzler had stumped all of those who entered.

Thirteen-year-old Leslie Hlavaty and two brothers from Chesterfield, 10-year-old Eric and 12-year-old Phillip Hsu, got all six of the December Math Puzzlers correct. Leslie was among a number of entrants from St. Gabriel Catholic School.

Eric goes to Wild Horse Elementary School and Phillip is at Crestview Middle School

Mr. Math Puzzler is Wayne Hesse, an 8th grade math teacher at Green Park Lutheran School in south St. Louis County. In December, he used a series of questions that were similar to some he'd used in the past.

That gave entrants an opportunity to look at past editions to check for the similar questions and their answers. With those past answers, there was also an explanation of how to arrive at those answers.

The Math Puzzler competition started in September, 2001. That means there are over two years of past Puzzlers--with answers--that can be checked. To do that, you just go to the Past Stories tab on the top of the home page and look at any editions from September, 2001, to the present.

Young Saint Louis.com likes it when there are kids who get all the right answers.

We not only name winner in this story. We also mailed a $10 Borders' gift certificate as a special bonus.

Here are the questions, answers and explanations for last month's Math Puzzlers:

The December, 2003, answers

1. Jim's pennies are worth as much as his nickels, his nickels are worth as much as his dimes and his dimes are worth as much as his quarters. If the total value of all his coins is $12, how many dimes does he have?

Answer: 30 dimes

The explanation: If each of the batches of coins are all worth the same, that means each batch is worth one-fourth of $12 or $3. That means there would be 30 dimes.

 

2. Four straight lines can cross in as many as six points (see diagram). What is the greatest number of points in which five straight lines can cross?

Answer: 10 points

The explanation: Here's an illustration of the answer:

 

3. Kevin is 14 inches taller than George. The difference between Kevin and Richard is 2 inches less than between Richard and George. Kevin at 6'6" is the tallest. How tall are Richard and George?

Answer: Richard is 6' and George is 5'4"

The explanation: With Kevin at 6'6" and 14 inches taller than George, George must be 5'4". Then, you divide the 14 inches so that one number is two more than the other. That makes Richard 6' even, which is six less than Kevin and eight more than George.

 

4. A baseball team just won a championship game and the players wanted to congratulate each other. They began shaking hands. How many handshakes were necessary for each player to shake every other player's hand? Remember, there are nine players on a baseball team.

Answer: 36 handshakes

The explanation: There are nine players. The ninth player shakes hands with the other eight. The eighth player has seven other players with which to shake hands.
This series can be set up in the following series of numbers:

     Player: 9 8 7 6 5 4 3 2 1
     Shakes: 8 7 6 5 4 3 2 1 - = 36 shakes

 

5. Two trains are on a head-on collision course. The trains are currently 65 miles apart. The north-bound train is traveling 55 mph and the south-bound train is traveling 80 mph. What is the distance between the two trains two minutes before they collide?

Answer: 4.5 miles

The explanation: The following formula will explain:

• One train will go 55/60th of a mile in one minute or 110/60th in two.
• The other train goes 80/60th of a mile in one minute, 160/60th in two.
• Both go 270/60th of a mile in two minutes, that's 4.5 miles.

 

6. A car travels at a speed of 30 mph over an unknown distance, and then returns over the same distance at a speed of 20 mph. What is the average speed for the total trip.

Answer: 24 mpr

The explanation: Distance equals time x rate (d=tr). To answer this question, you can pick any distance. We'll pick 60 miles so it matches up easily with 1 hour or 60 minutes. The 30-mpr car takes 2 hours to travel 60 miles. The 20-mpr car takes 3 hours. The two cars go 120 miles in 5 hours. The average speed is miles divided by time or 24 miles per hour.