Finding all the right answers
was elusive again in February

The search for six correct Math Puzzler answers turned out to be difficult again last month. No contestants answered all six correctly.

But, help is on the way.

Mr. Math Puzzler has some up with questions for March where the answers should be easier to find. Young Saint Louis.com wants to be able to award more prizes; we haven't had enough winners in previous months.

Those who enter the monthly contest and answer all six questions correctly will have their entries put in a hat and YSL.com will award up to three $10 Borders book certificates. To take part in the March competition, just click here.

Answers to February, 2002, Math Puzzlers

1. Which is larger: one-half times one-half of a dozen dozen or one-half dozen halved and cubed?

Answer: The first equation

The explanation:

½ x ½ = ¼ x 12 = 3 x 12 =36

OR

½ x 12 = 6 ÷ 2 = 3³ = 27

 

2. If two gallons of paint are required to cover all the faces of one cube, how many gallons will be required to cover all exposed surfaces of this figure, including the faces on the bottom. (All cubes are shown; there are no hidden cubes.)

Answer: 12 gallons

The explanation: There are 36 exposed sides (included those on the bottom) of the cubes in the illustration. If all six sides of one cube need two gallons of paint, then 36 sides in the illustration would need 12 gallons of paint.

 

3. You walk into a room where there are three boxes. One is marked "gold;" another marked "silver" and the third marked "gold & silver." You are told that all three labels are wrong. If you can figure out the correct contents of each box by looking at the contents of only one box, you can have all the gold and silver you can carry out of the room. How do you proceed?

Answer: Open gold&silver box

Explanation: If you open the gold&silver box, and it's silver, then the silver-marked box must be gold and the gold box must be gold&silver. But, if you open the gold box and it's silver, you still don't know which of the other boxes were gold or gold&silver. The same problem happens if you open the silver box first. You need to start with the gold&silver box first.

 

4. A local tennis tournament has 128 entrants for its singles competition. How many total matches will be needed to be played, including the championship match, to determine the champion?

Answer: 127 matches

Explanation: There's two ways to figure this. Since there are 127 entrants who lost, that means there were 127 matches. Or you can figure it this way: In the first round, there were 64 matches; second round, 32 matches; third round, 16 matches, fourth round, 8 matches; fifth round, 4 matches, sixth round, 2 matches, and seventh round, the final match. Thus, 64+32+16+8+4+2+1=127

 

5. What size square has a perimeter that is equal (in number only) to its area?

Answer: 4 x 4

Explanation: The only number where adding the four sides together will result in the same total as multiplying the number to get the surface area is 4.

 

6. Five friends are going to the movies. When they arrive, there are only six seats together left in the theater. The manager will let all five friends in for free if one of them can tell him how many different seating arrangements are possible for five people with six empty seats. All five were let in free. What was their answer?

Answer: 720

Explanation: This is called a permutation. The first person has six possible seat choices. The second person (since the first person is already seated) has five possible seats. Then, the third has four choices; fourth has three choices, and fifth has two choices. When you figure each of the five people could be the first one to pick a seat, that multiplies the possibilities. The permutation is arrived at by multiplying the 6, 5, 4, 3, 2. That comes to 720.