Four past winners got all the answers correct in the last Mr. Math Puzzler competition. The questions in the August edition were the final ones in the three-year run of the feature.

Those getting all six of the August Puzzlers correct were:

Zachary Bian, 11, of Grace Christian Academy; Rowland Han, 13, of Wydown School in Clayton, and brothers Eric Hsu, 10, and his brother, Philip, 12, both of Crestview School of Chesterfield School.

Because this is our last competition, Young Saint Louis.com is going to waive its 3-book-certificate rule and give $10 Borders' book certificates to all four winners.

Wayne Hesse, an 8th grade math teacher at Green Park Lutheran School, has been Mr. Math Puzzler for the last three years. The feature started in September, 2001.

During that time, there have been over 200 Math Puzzlers featured on YSL.com.

You can go back and try some by clicking on the Past Stories tab on the home page. Just pick any month after September, 2001. You can find the answers to each by jumping forward one month, and look for the Answer story.

YSL.com will continue to emphasize math in the coming months. Many of the articles in coming months will have math elements in them. We're also looking for another participatory math feature for your enlightenment and entertainment.

If any of you have any suggestions, be sure to offer them. You can e-mail us by clicking on the Your Turn tab on the home page and use the self-addressed e-mails offered there. If you want to send a snail-mail message, our office address is listed there.

Here are the answers and explanations for the August Puzzlers:

The Math Puzzler answers for August, 2004

1. What number should be removed from this list so that the mean of the remaining numbers is 6.1?

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

Answer: 5

The explanation: The sum of the 11 numbers is 66. Therefore, you'd need to subtract 5 to reduce that number to 61. Then, when divided by the 10 you'd end with a mean of 6.1.

 

2. When George took his place in the marching band, he noticed that he was 10th from the front, 7th from the back, 3rd from the left and 8th from the right in the rectangular formation. How many members were in the band?

Answer: 160 members

The explanation: If George is in the 10th row from the front and the 7th row from the back, it means there are 16 rows, front to back. If he's the 3rd from the left and the 8th from the right in his row, the row has 10 members. Therefore, 10 times 16 equals a 160-member band.

 

3. What is the remainder when the product (1492) (1776) (1812) and (1999) is divided by 5?

Answer: 1

The explanation: You can find this after without multiplying those four numbers, which would result in a very big number. You can do it by multiplying the ones digits of the four numbers (2 x 6 x 2 x 9) to get 216. Then, divide that number by 5 and the remainder is 1.

 

4. When the 171st positive even integer is subtracted from the 220th positive odd integer, the result is z, determine the value of z.

Answer: Z = 97

The explanation: First, multiply 171 by 2 to get 342. Then, multiply 220 by 2 and then subtract 1 to get 439. Then, subtracting 342 from 439, you get the answer of 97.

 

5. The energy saved from one recycled aluminum can will operate a television for 3 hours. How many aluminum cans would have to be recycled to furnish enough energy to operate 680 television sets for 4.5 hours per day for one week?

Answer: 7,140 can.

The explanation: This answer can be achieved easily by setting up a chart. The three columns include the Number of cans, the Number of TVs and the Hours. First, you have to figure that 4.5 hours a day equals 31.5 hours per week. Therefore, since one can powers a TV for three hours, it will take 10.5 cans to power one TV for 31.5 hours.

#Cans	#TVs	#Hours
1	1	3
680	680	3
7,140	680	31.5

 

6. Joan, Tim and Karen each start with the same positive number. Joan subtracts 1, doubles that result and then adds 2. Tim doubles his number, then subtracts 1 from the result and then adds 2. Karen subtracts 1 from her number, adds 2 to the result and finally doubles the answer. Who will get the largest final answer? (Hint: You can use any positive number to do this problem or, if you use some principles of algebra, you don't even need a number to figure which person has the largest final answer.)

Answer: Karen

The explanation: Again, a chart for each kid will help get the answer. Starting with x, work out the answer for each kid.

Joan	Tim	Karen
x	x	x
x-1	2x	x-1
2(x-1)	2x-1	x-1+2
2(x-1)+2	2x-1+2	2(x+1)
2x-2+2	2x+1	2x + 2
2x