Ben Harmon of St. Louis answered all six Math Puzzlers correctly in the September math competition. He's a first time winner.

The number of entries in September increased. That probably means kids were getting back into a math-mode with the start of school.

After all those graded math quizzes, Young Saint Louis.com's Math Puzzlers offer an opportunity to do some math just for fun. And, we don't even care if you get some help with your answers from older brothers and sisters.. or even parents, if they can help.

YSL.com believes having fun with math--without grading pressure--can help you learn more about math. And knowing the fundamentals of math is real important for your future.

The September puzzlers had a couple tricky questions. In one, there was no correct answer. We warned you about that. But, there was also Question 5. There, the time lapse during the first half of the parade review was one second less than the second half.

The Puzzlers for October are all word-and-number questions. There are no illustrations. (To look at the October questions, just click here.)

Here are the answers and explanations for the September Puzzlers:

The Math Puzzlers Answers
(September, 2002)

1. Remove only one matchstick to make the math correct:

Answer: Change + to -.

The explanation: The one matchstick that can make the difference is the vertical one that makes the "plus" sign. If you take off that matchstick, the "plus" becomes a "minus" and six (VI) minus (instead of plus) two (II) equals four (IV).

 

2. The local bottling plant recycles old bottles to make new ones at the rate of 10 old bottles to produce one new one. Remarkably, every bottle the plant produces gets recycled. Starting with 1,000 new bottles, how many bottles can be made if the bottles are recycled continually?

Answer: Either 1,111 or 111

The explanation: Remember, Mr. Math Puzzler was talking about continual recycling. The first batch of 1,000 bottles will recycle into 100 new bottles. When those 100 are returned and recycled, they will add another 10 bottles. Then, on the third recycling circuit, the 10 bottles will add one more bottle. Depending on whether you counted the first 1,000 bottles into your total or not, Mr. Puzzler says the answer could be either 1,000 + 100 + 10 + 1 = 1,111 or 100 + 10 + 1 = 111. He accepts either answer.

 

3. An entire group chartered a boat for the day for $840. Unfortunately, one couple had severe colds and had to cancel, so each person remaining had to chip in another $35. How many were there originally?

Answer: 8

The explanation: There's a trial-and-error way of figuring this. You can divide the original $840 charter cost by a variety of numbers. You're looking for a number that, if you subtract one couple, their share can be made up if each remaining person chips in an additional $35 each. Eight is a number that fits. Originally, each of the eight would pay $105 to make up the $840 fee. Then, if subtracting two, the six remaining would owe a total of $140, which is $35 more than their original contribution.

 

4. A messenger capable of running long distances set out to deliver a message so that reinforcements could be brought to help fight a horde of glubs. The messenger had to run for 24 miles. For two-thirds of the distance, he averaged 8 miles per hour. At what rate did he have to run the remainder of the distance in order to average 12 miles per hour for the entire journey?

Answer: No right answer

The explanation: Remember, Mr. Math Puzzler said there was one question without a right answer. The reason is the messenger, running at 8 miles per hour, ran two-thirds of the 24-mile distance in two hours. But, to average 12 miles per hour for the 24 miles, he would have had to do the whole distance in two hours. At 8 miles per hour, he'd used up the full two hours for just two-thirds of the distance.

 

5. An officer on horseback rides slowly down a line of 60 mounted troops placed 10 feet apart. Beginning with the first man, the officer takes 29 seconds to reach the 30th man. At that rate, how long will it take him to reach the 60th (last) man?

Answer: 59 seconds

The explanation: This answer is a little tricky. The officer took one second between each man. But, in the first 30, he actually started with number 1 so there were just 29 gaps between 1 and 30. But, in the second 30, there are 30 gaps because of the extra one from 30 to 31, so the second half took 30 seconds. There is not gap at the beginning between zero and 1.

 

6. Thirty-six coins will buy one knife, one sword and nine arrows. Two swords can be traded for one knife and four arrows. What is the price of each item purchased separately?

Answer: knife=2; arrow=3; sword=7

The explanation: This answer takes quite a bit of figuring. It involves two formulas and then the use of the subtraction method under the system of equations.

You know two things:

1. one knife, one sword and nine arrrows cost 36 coins and
2. two swords can be traded for one knife and four arrows.

Formula one:	36 = k + s + 9a
Formula two:	2s = k + 4a
Subtract:	-2s   -2s —————————  0  = k - 2s + 4a
Then Subtract:	36 = k + s + 9a - ( 0 = k - 2s + 4a) —————————————————————    36 = 3s + 5a

Then, we set up a substitution table for s and see what a and k need to be:(no fractions here):

s	a	k
1	x
2	6	x
3	x
4	x
5	x
6	x
7	3	2

Until you equate 7 coins to one sword, there's no way to solve the second formula. But, with the 7, 2 swords equals 14 coins and it's possible to solve assign 3 coins to each arrow and 2 coins to the knife. Thus
      2s (14) = 4a (12) + k (2)

Then you substitute those numbers to the first formula:
      36 coins = k (2) + s (7) + 9a (27)