The number of entries in Young Saint Louis.com's Math Puzzler contest increased during October. But, Question 6 proved to be too much.

All but one of the entrants answered that question incorrectly. And, the one kid with the correct answer to Question 6 missed other answers.

Several entrants got five of the six Puzzlers correct.

At first glance, Question 6 looked pretty easy. But, it turned out to be a toughie.

Wayne Hesse of Green Park Lutheran School is our website's Mr. Math Puzzler. When asked about Question 6, he suggests each contestant look for a general principle of math before answering a question.

In this case the math principle says: "You can't average averages."

Question 6 gave the average speed per hour for each trip segment. But, you needed to go back to find the time it took the biker to cover the distance of each segment before giving the answer. (Look below to see two different ways to answer Question 6. The answer is 10 kilometers per hour.)

Remember, all those answering all six Puzzlers correctly will have their names published the following month. Also, all winning entries will be put into a hat and up to three $10 Borders book certificates will be awarded.

Answers to October, 2001, Math Puzzlers

1. What is the sum of the spots on the left side of the stack of dice?

Answer: 11

Explanation: You look at the hidden left side of the dice to find the number of spots. For future reference, remember the opposite faces of a six-sided die always add up to seven.

 

2. What is x?

1+2=5
2+3=13
4+5=41
5+6=61
6+7= x

Answer: 85

Explanation: The relationship of the other numbers is that both numbers on the left side of the = signs have been squared first before they are added.

 

3. What is the total of these six fractions?

1/3 + 3/1 + 3/6 + 6/3 + 4/8 + 8/4 = ?

Answer: 8 1/3

Explanation: You need to express these fractions with a common denominator before adding them. The common denominator is 24 and the numerators then add to 200. When that is divided by 24, you get 8 1/3.

 

4. Suppose you have two egg timers, a five-minute and a three-minute. How can you use these two measuring devices to time an egg that would be boiled for exactly two minutes?

Answer: Start both timers at the same time and, when the three-minute timer goes off, put the egg in boiling water. Then, when the five-minute timer goes off, it will have been two minutes.

 

5. Add arithmetical symbols (+, -, x, (divide symbol) between the numbers on the left side of the equals sign to make the equation true.

1 2 3 4 5 6 7 8 9 = 100

Answer: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 x 9 =100

Explanation: Some of you found other combinations using +, - and x to get to 100.

 

6. Timothy is riding a bicycle on a road that can be thought of as having four equal parts. On the first fourth, which is level, he pedals at 10 kilometers per hour. On the second fourth, which is on an upslope, he pedals 5 kilometers per hour. On the third fourth, a downward slope, he goes 30 kilometers per hour. On the final fourth, which is level again but with a tailwind, he goes 15 kilometers per hour. What is Timothy's average speed?

Answer: 10 kilometers per hour

Explanation: You can figure this either with arithmetic or with algebra.

With arithmetic reasoning, pick a common distance for each segment, such as 10 kilometers. Thus, the first segment at an average of 10 kpr takes 1 hour or 60 minutes. The second segment at 5 kpr takes two hours or 120 minutes. The third segment at 30 kpr takes just 20 minutes. The fourth segment at 15 kpr takes 40 minutes. That's a total of 240 minutes or four hours. The number of minutes divided by four (representing the four segments) is 60 minutes, or 10 kilometers per hour.

With algebra reasoning, you express that as:

Distance is L.

Total time is 

   L     L     L     L
  --- + --- + --- + ---
   10    5     30    15


  3L   6L   L    2L 
  -- + -- + -- + --
  30   30   30   30


  12L
  ---
   30


   2L
   --
    5
                     

       distance
Rate = --------
         time
                     

        (4L) 
Rate = ------
       (2L/5)
                     

       (20L)
Rate = -----
       (2L)
                     

Rate = 10