We've got a first-time Math Puzzler winner

Stephanie Roberts of Florissant answered all the August Math Puzzler questions correctly. She's a first-time winner in the "fun math" competition.

The stumbling block for other entrants was the visual Question 4.

August marked the end of the first year for Mr. Math Puzzler on the Young Saint Louis.com website. We started the Math Puzzlers last September at the start of the 2002-2003 school year.

We began the Math Puzzlers for two reasons. First, we wanted to have more YSL.com features where you — the readers — could participate. Second, we wanted to give kids a chance to have some fun with math--without having to worry about whether you'd get a good grade.

But, just because the Math Puzzlers are outside the classroom, you might get a chance to get some extra-credit in school.

Why not suggest to your math teacher that he or she give extra credit to any one answering each month's questions and sending in the entry. Maybe your teacher might like to collect all the entries and send them in as a group.

Then, if anyone gets all the answers correct, that might be worth some extra-extra credit. Suggest that to your teacher today. Also, entrants who get all answers correct have an opportunity to get a $10 Borders gift certificate.

(Before trying for this month's answers, why not check previous questions--and answers. Just click on Past Stories at the top of the home page and look up past questions and answers. Math Puzzlers started in September, 2001, and those answers were in October, 2001.)

(Since this edition is the start of the second year for Math Puzzlers, you have 12 sets of questions and answers to review. By checking past questions and answers, you'll get an idea how Mr. Math Puzzler thinks.)

To enter the September competition, just click here.

Now for the answers to last month's Puzzlers:

Answers to August, 2002, Math Puzzlers

1.) Six sterling silver teaspoons and six soupspoons cost $300, but three soupspoons and nine teaspoons cost $270. How much would a dozen teaspoons cost?

The answer: $240

The explanation: Here are both the algebraic formula method and trial-and-error methods for finding the answer. First, trial and error. If six tsps and six soupspoons cost $300 and nine tsps and three soupspoons cost $270, it means the tsps cost $10 less than the soupspoons. That means the tsps cost $20 and the soupspoons cost $30. Therefore, 12 tsps cost $240.

Using the addition method under the system of equations:

6t + 6s = 300 -2(9t + 3s = 270)   (Multiply the second equation by -2 to clear one variable.)

6t + 6s = 300 -18t - 6s = -540 --------------- -12t      = -240 ----        ---- -12          -12                 t = 20

 

2.) If you reverse the digits of Rachel's age, you will have the age of her grandmother. Her grandmother's age also is the two digits of Rachel's age added together and then squared. What are their ages?

The answer: 18 and 81

The explanation: This is a good trial-and-answer question. First, we know Rachel's age is two digits, so she's over 10. With trial and error, you start with the numbers that make sense. For instance, if Rachel is 15, her grandmother could be 51. But, squaring 1 plus 5 won't yield 51. But, Rachel at 18 would work. Her grandmother could be 81 and 1 plus 8 squared is 81.

 

3.) After your guests leave and you are cleaning up, you find an equal number of dimes, quarters and nickels under the sofa cushions totaling $8. How many of each coin did you find?

The answer: 20 of each

The explanation: This question opens the way for either an algebraic or a trial-and-error answer. With trial and error, you start with the number of each coin it takes to make $8. That's 80 dimes, 24 quarters and 160 nickels. Starting with 10 each, you won't get an equal number of three coins to add to $8. Keep going. When you get to 20 each, you'll have 20 dimes at $2, 20 quarters at $5 and 20 nickels at $1.

For a formula, use this:

.05x + .lx + .25x = 8

              .4x = 8
                —   -
               .4  .4

                x = 20

 

4.) Which diagram in the bottom row best completes the sequence when placed in the right-hand position in the top row?

Answer: diagram C

The explanation: This is a visual thing. There are actually two patterns at work here. First, on the top line, the second and third circles have asterisks and the shaded segments just opposite each other. The left hand circle in the top row has the asterisk in the upper left and the shaded segment in the upper right. Diagram C has the asterisk in the upper right and the shaded segment in the upper left.

Another way to look at it, think of the asterisks in the top row as a sequence that is rotating 90 degrees counter clockwise and the shaded segments as a sequence rotating 90 degrees clockwise. Again, Diagram C is the one that completes those sequences.

 

5.) There is an unknown number of hideous monsters known throughout the land as glubs. Glubs live underground but can rapidly burrow to the surface if they smell a human--one of their favorite treats. Between them, Garbus and Hylar, two knights, have slain 24 glubs. Garbus has killed four more glubs than Hylar has killed. How many glubs has each man slain?

Answer: Hylar, 10; Garbus, 14

The explanation: Here are two ways to figure. First, trial-and-error. If they had slain the same number, each would have slain 12. For Garbus to have four more, that would mean increasing Garbus to 14 and dropping Hylar to 10.

Using a substitution method of the system of equations, with g as Garbus and h as Hylar:

g + h = 24 or
g = h + 4

(h+4) + h = 24

   2h + 4 = 24
                -4   -4
       --   --
       2h = 20
       --   --
        2    2

        h = 10

 

6.) While out exploring, a group of girls came upon an apple tree whose fruits were ripe for the picking. One of the girls climbed the tree and picked enough apples for each girl to have three, with none left over. Then, along came three boys, making it impossible to divide the picked apples evenly. However, after picking one more apple and adding it to the total, each child had two apples with none left over. How many apples were divided among how many children?

Answer: 16 apples among 8 kids

The explanation: A key is to remember you don't know the number of girls in the group. Don't just assume it was three girls just because three boys showed up. By trial and error, if one girl picked three apples for each girl, the possible ratios could be two girls and six apples, three girls and nine apples, etc. Then, you know three boys were added to the group and one more apple would allow all kids to have two apples each. The number works with five girls and 15 apples and then 8 kids and 16 apples.

Using an algebraic formula with g for girl,

 3g + 1 = 2(g + 3)
 3g + 1 = 2g + 6
-2g      -2g
---      ---
  g + 1 =      6
     -1       -1
     --       --
  g     =      5