Brothers Eric and Phillip Hsu of Chesterfield seems to have the Math Puzzlers figured out. Both are past winners and they also got the six September Puzzlers correct.

And that's even after Mr. Math Puzzler worked on some new and unique math propositions for the start of the third year of the competition.

The Hsus were the only entrants to get all six answers correct. So, both of them win $10 Borders book certificates.

Under Math Puzzler rules, up to three winners get a chance to get book certificates. If more than three get all the answers, the entries are put into a hat and three are selected for the book certificate bonus.

If you want to try your hand at answering the Math Puzzlers, you might like to review past questions and answers to find out how Mr. Math Puzzler thinks.

Using the Past Stories tab on the home page, pick any past issue of YSL.com since September, 2001. That way, you can use past stories to review previous questions and answers. The answers to one month's questions are included in the next month's edition.

When you think you're ready, come back to this October entry and try your luck.

A reminder: These Math Puzzlers can be quite challenging, especially for younger kids. Remember, we don't mind if you get help from a parent or older brother or sister. In fact, you might want to make this a family activity.

The September, 2003, Puzzler answers

1. Adam and Betty Brown and Charles and Dolores White were having dinner at a restaurant. During dinner, they discussed their weights. Adam said, "I weigh 60 pounds more than Betty." Charles said, "I weigh 40 pounds more than Dolores." Then Adam said, "Together, Betty and I weigh 40 pounds more than you and Dolores." Together the Browns and Whites weight 720 pounds. How much does each person weigh?

Answer: A=220, B=160, C=190, D=150

The explanation: You start with Adam being 60 lbs. heavier than Betty (a = b + 60) and Charlie being 40 lbs. heavier than Dolores (c = d + 40) Then proceed with the following equations that involve collecting like terms:

First equation:

  b + 60 + b =   d + 40 + d + 40
 2b + 60     =  2d + 80
         -2d   -2d
         ---   ---
 2b + 60 -2d =       80
     -60            -60
     ---            ---
 2b     - 2d =       20

Second equation:

   b + 60 + b +  d + 40 + d = 720
  2b + 100    + 2d          = 720
     - 100                   -100
     -----                   ----
  2b          + 2d          = 620

Then:

       2b - 2d =  20
  plus 2b + 2d = 620
       -------   ---
       4b      = 640

      (4b)/4   = (640)/4

      (Betty)b = 160

Once you find Betty's weight, the others can be computed easily.

 

2. There are 10 bags of silver coins. Each bag contains a different number of coins of 15 or more. One of the bags contains all counterfeit coins which look exactly like the others but each one weighs 1 gram less than the real ones. Each real coin weighs 10 grams. Using a scale only once can you determine which bag contains the counterfeit coins?

Answer: See explanation

The explanation: If each real coin weighs 10 grams, then each counterfeit coin would be 9 grams. Now, number the bags. Take one coin from Bag 1, two coins from Bag 2, three from Bag 3, until you've taken 10 coins from Bag 10. Then, put those coins on the scale and weigh them. If the total weight of the coins is one gram less than the total number times 10, it means the counterfeit coins are in Bag 1. If the total weight of coins is five grams less, it means the counterfeit coins are in Bag 5. By this method you can determine which bag as the all counterfeit coins.

 

3. While talking at a barber shop the other day, several old-timers were discussing how tough things were in the Depression days of the 1930s. In the early days of the motion picture industry, to stimulate business during the Depression, tickets for adult admissions were 25 cents and children's tickets were only a dime. With each children's ticket, a free lollipop was given to each child. On one particular evening, the ticket seller reports that he sold exactly 300 tickets and took in $55.65. How many free lollipops were given out that night?

Answer: 129

The explanation: Again, use equations with "a" for adult tickets and "c" for kids:

a +   c  =300 -4 (.25a + .1c) =55.65

a +   c = 300 -a - .4c = 222.6 --------   -----      .6c = 77.4      ---   ----      .6      .6        c = 129

There were 129 children's tickets sold, thus 129 lollipops given out.

 

4. Assume that the earth is a perfect sphere and that you have a long belt stretched tightly around the equator which is 24,900 miles long. How much length would you have to add to the belt to raise it one foot away from the surface of the earth all the way around?

Answer: 6.28 feet

The explanation: Circumference is "c" and diameter is "d".

     c = (pi)d
     c = 3.14(d+2)
     c = 3.14d + 6.28
     The answer is 6.28 feet.

 

5. George now has $1,066.41 in an account at his bank at 8% annual interest rate compounded quarterly. How much money did he have six months ago?

Answer: $1,025

The explanation: If you want to back off the interest, you can do it by dividing the total by 1.02% since the money earned 2 percentage points for each quarter. Thus, subtracting one quarter would be $1,066.41 divided by 1.02 or $1,045.5. You want to go back two quarters, so you divided again by 1.02 and get $1,025.

 

6. Divide this polygon in four smaller polygons of equal size and shape.

Answer: See explanation figure

The explanation: