No one solved the July Math Puzzlers

The Math Puzzler questions were too much for entrants in the July competition.

Especially, it was the Roman numeral question (Question No. 3) that stumped everyone. The complexity of the Roman number system is pretty high when it comes to large numbers.

Maybe that's why the Romans, along with many other people, moved over to the Arabic numeral system (1, 2, 3, etc.)

You've got another chance to participate in the Math Puzzler contest. Just click here to get to the August questions. Use the handy entry form and enter today.

(If you are just starting with Math Puzzlers, you might like to check questions and answers from the past. We've had Math Puzzlers since September, 2001. You can reach back by clicking on the Past Issues tab on the home page and check past editions. Remember, the answers to each month's questions are in the next month's issue.)

Here are the answers to the July questions:

Answers for July, 2002, Math Puzzler Contest:

1. How far do you have to count before using the letter A in the spelling of a number?

Answer: 1,000

The explanation: The word "thousand" is the first one with the letter "a" in it.

 

2. Make 1,000 by using exactly eight 8's. You may use any operation signs between the numbers that you need.

Answer: 8+8+8+88+888=1,000

The explanation: Mr. Math Puzzlers' answer used only one operating sign (+). But, entrants used multiple signs and got the right answer with only eight 8's. Examples include (8x8)+(8x8)x8-8-8-8=1,000 or (8888-888) divided by 8=1,000.

 

3. Change the ZIP code 63125 from Arabic numerals to a Roman numeral. (Hint: Because we don't use large Roman numerals very often, you might want to check in the front or back of a big dictionary to see how to handle numbers that go into the many thousands.)

Answer:

The explanation: As you know, in Roman numerals, I is one, V is five, X is ten; L is 50; C is 100, D is 500 and M is 1,000. When you get into many thousands, an overline is used to designate multiple-thousands. Thus, (with the overline) is 63,000. Then the non-overlined CXXV is the 125 in the ZIP code.

 

4. Gareth collects winged cats. One day, a friend asked him, "How many winged cats do you have now, Gareth?" Gareth answered, "I have two-thirds of their number plus two-thirds of a winged cat." How many winged cats does Gareth have?

Answer: 2 winged cats

The explanation: Two-thirds of 2 is 1 1/3. Then, add 2/3 to get a total of 2 cats. In formula form, it would be like this (with X being number of winged cats):

2/3 X + 2/3 = 3/4 X

Eliminate 2/3 X on both sides to get 2/3 = 1/3 X

Then 3(2/3) = 3(1/3 X) or 2=X

 

5. Jarblek, Belgar, Poklgar and Garion were each paid the same hourly rate to build a bridge. One day, Jarblek worked the full day, Belgar worked half of a day and Poklgar worked half as long as Belgar and one third as long as Garion. Together the four earned 40 lucs. How many lucs did each receive?

Answer: J gets 16; B gets 8; P gets 4 and G gets 12

The explanation: J works 1 day; B works 1/2 day, P works 1/4 day and G works 3/4 day. That's a total of 2 1/2 days of work or 16 lucs per day. Then, factor in the time each person worked to get the lucs per person. In formula form (with P being the total pay for one day's work):

1 P + 1/2 P + 1/4 P + 3/4 P =40

4/4 P + 2/4 P + 1/4 P + 3/4 P = 160/4

10/4 P = 160/4   or   10 P = 160   and   P = 16 lucs

 

6. A knight on horseback left Belft to ride to Dalch at the same time another knight left Dalch on horseback to ride to Belft along the same road. The first knight traveled 30 miles per hour and the second knight traveled 28 miles per hour. How far apart were the two knights one hour before they met?

Answer: 58 miles

The explanation: You had to be careful with the wording of this question. It doesn't ask the distance between Belft and Dalch. It asks how far apart the two knights are an hour before they meet. Since one is traveling 30 miles per hour and the other is moving 28 miles per hour, they'll travel a total of 58 miles in that hour before they meet.