The Hsu brothers win again in February

We may have to give Eric and Phillip Hsu a permanent trophy in the Math Puzzler competition. The two brothers from Chesterfield again got all the Puzzler questions correct in February.

That marked the third consecutive month the two brothers answered all the Puzzlers correctly. The two also won in December, 2003, and January, 2004.

In February, they were the only two entrants who had the right answers for all six. Therefore, both get the bonus prize of $10 Border book certificates.

Under the simple YSL.com rules, the contestants who get all six answers correct have their names published the following month. And, YSL.com also provides gift certificates for up to three winners.

We had some first-time entrants in the February Puzzler contest. One of them was able to answer all but one of the questions correctly.

Mr. Math Puzzler is Mr. Wayne Hesse from Green Park Lutheran School. He comes up with a wide assortment of Math Puzzlers each month.

Why don't you ask some of your friends to enter the fun competition. Maybe you can make a Math Puzzler party and all try to answer the March questions correctly.

Before entering, you might like to look at past questions and answers. You can do that by going to the Past Stories tab on the home page. Look up any edition since September, 2001, and click on to the Math Puzzler answer story.

The article will give you the questions and detailed answers on how you could arrive at the correct answer.

Then, you'll be ready to enter the March competition. To get the March entry blank and questions, just click here.

Here are the answers to the February Puzzlers:

February Math Puzzler answers

1. What fraction of the numbers from 1 to 1,000 have the digit 7 as at least one of the digits?

Answer: 271 of 1,000

The Explanation: Except for the 700s, there are 19 numbers in each 100 which have the digit 7 as at least one of the digits. Nineteen times 9 is 171. Then, all the numbers in the 700-799 sequence have a 7. So, 171 plus 100 equals 271 of the 1,000 numbers.

 

2. How many zeros are at the end of the whole number 100(!)? (Example, 100 times 99 times 98 times 97 times.... times 2 times 1)

Answer: 24 zeroes

The explanation: 100(!) is read as one hundred factorial. In figuring the number of zeroes, remember that every time there is a 5x2 there will be a number ending in zero. So there are 20 multiples of 5 from 1 to 100 (Such as, 5, 10, 15, 20.....100) But, there are also 4 double multiples of 5. (Such as 25, 50, 75 and 100) So 20 plus 4 is 24.

 

3. An ice cream store advertises 31 flavors of ice cream. How many different double-decker cone combinations are possible if both flavors have to be different? (It doesn't matter which flavor is on top or on the bottom.)

Answer: 465

The explanation: This is a matter of determining math permutations. You want to know how many combinations of 31 flavors that are taken two at a time. The answer is 31 times 30 equals 930 and then divided by two or 465.

 

4. What is the ones digit of 7¹⁹⁹⁸?

Answer: 9

The explanation: You don't need to go through the entire sequence 1,998 times. Rather, set up a chart and look for patterns that develop as you go along. For instance,

     7 to the first = 7
     7 to the second = 49
     7 to the third = 343
     7 to the fourth = 2,401
     7 to the fifth = 16,807
     7 to the sixth = 117,649
     7 to the seventh = 823,543
     7 to the eighth = 5,764,801

Right away, you see there is a pattern of having the ones digit show up as a recurring 4-number sequence of 7, 9, 3, 1. Then, in going to the 1998th power, you will run through that sequence 499 and 1/2 times. The number nine is the second in the four-number pattern. Therefore, the ones digit at 7 to the 1998 power will be 9.

 

5. One news carrier can deliver 75 newspapers in 2 hours. How many papers can 4 carriers deliver in 4 hours?

Answer: 600 papers

The explanation: Mr. Math Puzzler likes to figure these answers by using a chart:

Carriers	Papers	Hours
1	75	2
4	300	2
4	600	4

 

6. How many rectangles can you find in the grid shown? (Hint: Remember a square is a special kind of rectangle.)

Answer: 60 rectangles

The explanation: This is another that lends itself to a chart form so you can keep track of the number of various sized rectangles.

1x1 size: 12	1x2 size: 17	2x3 size: 7
2x2 size: 6	1x3 size: 10	2x4 size: 2
3x3 size: 2	1x4 size: 3	2x4 size: 1
-- 20	-- 30	-- 10 for total of 60