The number of entries in the July Math Puzzler contest were down, probably because of summer vacation. But, there was one winner and he's a familiar face.

In June, 2003, Thomas Van Horn was included twice in Young Saint Louis.com. First, he was featured in a story about his efforts to send "care" packages to U.S.troops in Iraq.

Then, he was also one of two winners in YSL.com's Harry Potter Trivia contest.

This month, he's back as the only winner in the July Math Puzzler competition. As a result of answering all six Puzzlers, Thomas gets a $10 Border's book certificate as well as having his name in this article.

In keeping with summer, Mr. Math Puzzler, math teacher Wayne Hesse of Green Park Lutheran School, loosened up a bit in July.

There were two questions based on grids where it was possible to have more than one correct answer. Another answer called for an illustration, rather than a formula.

But, the one that gave most entrants trouble (Question 2) involved the ticking of a clock. It sounded simple, but Mr. Math Puzzler made it a little tricky.

YSL.com is continuing the Math Puzzlers during the summer. That's so you can have some fun but still keep up your math skills. Getting friends together in the shade of a big tree would be a good way to spend a hot summer day.

You could make a little competition out of it and then all send in your entries.

If you or your friends haven't entered before, you might like to review some past Puzzlers to learn how Mr. Math Puzzler thinks.

YSL.com Math Puzzlers started in September, 2001. Using the Past Stories tab on the home page, pick a past month or two. Then, you can review past questions and check answers the next month.

(Once you've studied up, you can move to the August quiz by clicking here.)

The July Answers:

1. The dragons Argothel and Bargothel like to get together for fiery conversations. They live some distance apart, each in his own cave. One day, Argothel left home to visit Bargothel at exactly the same time that Bargothel left home to visit Argothel. The day being most agreeable, both dragons decided to proceed at a rather leisurely rate. So, rather than fly, they walked. Argothel walked at a constant rate of 24 miles per hour and Bargothel at a constant rate of 36 miles per hour. How far apart were they five minutes before they met? (We've had a similar question to this one in the past.)

Answer: Five miles

Explanation: If Argothel walks at 24 miles per hour, he would travel two miles in five minutes. If Bargothel travels 36 miles per hour, he would travel three miles in five minutes. So, in the final five minutes, Argothel would travel an additional two miles while Bargothel would travel an additional three miles. Thus, with five minutes to go, that leaves them five miles apart.

 

2. We have an old-fashioned grandfather clock that strikes the exact number of times each hour to indicate the correct time. It takes 15 seconds to strike 6 o'clock. How long will it take to strike 12 o'clock?

Answer: 33 seconds

Explanation: This one is a little tricky. The timing starts when the first chime sounds. Thus, to get to 6 o'clock, there are six sounds with five silent spaces of three seconds each between the first and sixth sound. But, for 12 sounds there are 11 3-second gaps or 33 seconds, not 30 as might seem logical at first glance.

 

3. Place the numbers one through eight in the squares shown so that no consecutive numbers occur next to each other in adjoining squares either vertically, horizontally or diagonally.

Answer: There are more than one
possibility, as long as no consecutive
numbers occur next to each other.

Explanation: One possibility:

       7
     3 1 4
     5 8 6
       2

 

4. Can you take the digits 1 through 9 to form the numerator and denominator for a fraction that is equal to 1/2?

Answer: This also has more
than one correct answer

Explanation: Two possibilities:

       6 7 2 9   1
     --------- = -
     1 3 4 5 8   2

or

       7 3 2 9   1
     --------- = -
     1 4 6 5 8   2

 

5. There once was a very artistic farmer with 10 fruit trees. He wanted to plant them in five straight rows with 4 trees in each row. How did he lay out his orchard? (Remember, there is no numeric answer. Your answer must be in the shape of the orchard's design.)

Answer: This solved best
by a star diagram

Explanation: With the star shape, trees can be a part of more than one straight line.

6. A water tower has three drains. One drain could empty the tank in 45 hours, one in 15 hours and the third one in 30 hours. How long would it take to empty the tower if all three drains were opened? (This is not going to give you a nice even-numbered answer.)

Answer: 90/11 or 8 2/11 hours

Explanation: This involves finding a cross product, then multiply and divide. One drain empties 1/45th of the tank in one hour; another, 1/15th in an hour, and the other, 1/30th in an hour. The formula is then:

      1    1    1   1
     -- + -- + -- = -
     45   15   30   T

      2 + 6 + 3   1
      --------- = -
         90       T

         11   1
         -- = -
         90   T

then, develop a cross product

        90 = 11T

or

8 2/11 hours = T