Two more Math Puzzler winners in April

Just as in March, we had two winners in the Math Puzzler competition. Both of those were answered all six questions correctly in April were first-time winners.

The April winners were Jessica Cunningham and Kimberly Guardado, both of St. Louis.

Young Saint Louis.com congratulates both Jessica and Kimberly. And, as a special bonus, each of them will receive by mail a $10 Borders gift certificate.

Several other entries had five of six answers right. The question that stumped them was Puzzler 2, about the woman's age.

The April winners marked the second month in a row that we've had two winners.

We hope those who have entered before will encourage their friends to try also. It's easy to enter; just print out the May entry form and questions, write in the answers and mail them to us.

To see the May Puzzlers, just click here.

Now, for the answers to the April Puzzler competition:

Answers to April, 2002, Math Puzzlers

1. If you built a rectangular pyramid with the bottom being a square, using ping-pong balls, how many ping-pong balls would there be in a pyramid with seven layers with only one ball at the top?

Answer: 140 balls

The explanation: It will take four ping-pong balls (4) on the second layer to hold up the one ping-pong ball on the top layer and keep the pyramid square. Then, it takes three balls per side (total of 9) in layer three to support the second layer; four balls per side (total of 16) in layer four to support layer three; five balls per side (total of 25) in layer five to support layer four; six balls per side (total of 36) in layer six to support layer five, and seven balls per side (total of 49) to support layer six. Add 1, 4, 9, 16, 25, 36 and 49 and you get the answer of 140 balls.

 

2. A woman turned to her friend and said, "Three years from now, I'll be three times as old as I was 27 years ago. How old is the woman now?

Answer: 42

The explanation: The easiest way to explain this is with an algebra formula. In this, N will be the age we want to discover. There are five layers to the answer:

1. N + 3 = 3(N-27)
2. Multipling N - 27 by 3: N + 3 = 3N - 81
3. Eliminate 81 from equation: N + 84 = 3N
4. Eliminate one N from both sides: 84 = 2N
5. Divide both sides by 2: 42 = N

 

3. If you have a full glass of water and pour out half, then pour back in half of what you poured out, pour out a third of what you now have and pour back in a third of a glass, what fraction of the glass is full?

Answer: 5/6ths

The explanation: If you pour out one half of a full glass, you have one-half left. Then, pouring back one-half of what you poured out brings it back to three-fourths. Then, pouring out one-third gets you back to one-half. Then, putting one-third of a full glass comes out 1/2 + 1/3 = 5/6th.

 

4. See if you can determine the logic needed to provide the missing numbers in the last circle.

Answer:     

The explanation: You need to establish the pattern of increases in the numbers of all three segments. In the upper left, the 3 to 8 is an increase of five, 8 to 15 is an increase of seven, 15 to 24 is an increase nine. That indicates the next jump would be by 11 or 35. In the upper right, the sequence is 4 to 9 or five; 9 to 16 or seven, 16 to 25 or nine and then the next number would increase by 11 or 36. In the bottom segment, the increase is first 6, then 8, then 10 and finally by 12 or 42.

 

5. A picture frame that usually sells for $50 is on sale for 5% off. If a 5% sales tax were added to the sale price, what amount would be owed?

Answer: $49.88

The explanation: A 5% discount off $50 brings the sale price to $47.50. Then, a 5% tax on the $47.50 sale price is $2.375 (rounded to $2,38). That added to $47.50 makes the total $49.88.

 

6. Four friends--Dave, Mike, John and Terry--are nicknamed Stick, Batman, Atomic Head and Feaser, but not in that order. What is the nickname of each?

a. John is faster than Batman, but not as strong as Atomic Head.
b. Batman is stronger than Terry, but slower than Feaser.
c. Dave is faster than both John and Stick, but not as strong as Batman.

Answer: Dave=Atomic Head
Terry= Stick
John=Feaser
Mike=Batman

The explanation: A good way to determine this answer is by using a matrix and, by a process of elimination, use the clues to determine which guy matches up with which nickname.

	A.H.	Stick	Feaser	Batman
John	X1	X3	O	X1
Terry	X	O	X2	X2
Dave	O	X3	X	X3
Mike	X	X	X	O

 

1. Using first clue, you know John can't be Batman or can't be Atomic Head.
2. Using second clue, Terry can't be Feaser or Batman
3. Using third clue, Dave can't be Stick or Batman.
4. Then, checking the matrix you can see John is Feaser.
5. Checking further, Mike has to be Batman.
6. Then, the only two boxes open are Dave at Atomic Head and Terry and Stick.