Quiz Question

Number 169 of a continuing series

Martin Gardner died eight years ago, but he left behind a treasure of his writings. Here is from one of his books.

SMITH DROVE at a steady clip along the highway, his wife beside him. “Have you noticed,” he said, “that those annoying signs for Flatz beer seem to be regularly spaced along the road? I wonder how far apart they are.” Mrs. Smith glanced at her wrist watch, then counted the number of Flatz beer signs they passed in one minute. “What an odd coincidence!” exclaimed Smith. “When you multiply that number by ten, it exactly equals the speed of our car in miles per hour.” Assuming that the car’s speed is constant, that the signs are equally spaced and that Mrs. Smith’s minute began and ended with the car midway between two signs, how far is it between one sign and the next?

Gardner, Martin. My Best Mathematical and Logic Puzzles (Dover Recreational Math) (Kindle Locations 347-354). Dover Publications. Kindle Edition.

No fair going to the book for the answer. Post your answer as a comment below.

Quiz Question

Once again I turn to Martin Gardner’s book for a Quiz Question.

AN AIRPLANE FLIES in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

No fair going to the book to look up the solution. Post your answer in the comments section below.

Update and solution

And Greg has the correct answer. See the comment below. Mike has the correct answer, as well, since the question only asked whether greater, less, or the same.

Quiz Question

Here’s another from Martin Gardner. You can purchase the book and look up the answer, or you can (preferred) work this one yourself.

A SQUARE FORMATION of Army cadets, 50 feet on the side, is marching forward at a constant pace. The company mascot, a small terrier, starts at the center of the rear rank [position A in the illustration], trots forward in a straight line to the center of the front rank [position B], then trots back again in a straight line to the center of the rear. At the instant he returns to position A, the cadets have advanced exactly 50 feet. Assuming that the dog trots at a constant speed and loses no time in turning, how many feet does he travel?

Post your answer in the comments section below.

Quiz Question

This one is from a book by Martin Gardner, so no fair going to the book for the solution.

In the diagram you see four bugs. they are on the corners of a square 10 feet on a side. Each bug looks at a bug on the adjacent corner and crawls directly toward that bug. Of course, the other bug is also moving, so each bug has to constantly change course to keep heading toward the other bug. The bugs crawl at a constant speed, the same for all.

  1. Do the bugs ever meet?
  2. If the bugs meet, how far does each bug travel?

Post your answer in the comments section below.

Update And Solution

The problem was designed to throw people off by means of distraction. Your first thought in attacking this is you’re going to have to compute the length of a spiral. In contrast, the approach is greatly simplified.

Start by taking a bug’s eye view, literally. Each bug sees another bug, at ten feet away at the start, and traveling perpendicular to the bug’s line of sight. That means the bug being looked at is not coming closer nor getting further from the bug traveling at him. And the situation never varies. Each bug is always going straight at another bug, and the closure rate is always due to the bug’s walking speed. So each bug keeps closing the ten-foot distance at a constant rate and travels 10 feet total to reach the other bug. And that’s the solution to the problem.

What might confuse people is that the total number of turns in the spiral is infinite, seeming to pose an intractable problem. It’s one of the interesting aspects of mathematics.

Quiz Question

Another one from the Internet. People, I don’t think these up, myself:

Huge pie. A huge pie is divided among 100 guests. The first guest gets 1% of the pie. The second guest gets 2% of the remaining part. The third guest gets 3% of the rest, etc. The last guest gets 100% of the last part. Who gets the biggest piece?

Submit your answer in the comments section below.

Quiz Question

An easy problem. The area of the large circle is 10. What is the combined area of the two semicircles? Prove it. Post your answer as a comment below.

Update and solution

You can resolve this one without doing any math. The solution is in how the question is posed. It is posed that there is a solution, but the sizes of the two semicircles are not specified. Therefore the answer is the same for all configurations of the two semicircles, including the case where the yellow semicircle takes up half the area of the large circle, and the blue semicircle disappears. Therefore the answer is that the sum of the areas of the two semicircles is ½ the area of the large circle.

Quiz Question

I stole this one off the Internet, and I’m not telling where I got it. No fair using Google to find it.

    There are 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins. How to find the false coin by three weighs on a simple scale?

Post your solution in the comments section below.

Quiz Question

The picture says it all. What fraction of each shape is shaded? This one is on the Internet, so no fair hunting it down. Post your answer as a comment below.

Update and Solutions

I’m going to settle this week’s Quiz Question today so I can start looking for one for next week. Here are my solutions, from left to right.

This is the only one that requires some math, despite what top diagram promises. I have drawn an arrow across the width of the blue hexagon to show that it is the same width as the length of a side of the outer hexagon. It’s left to the reader to  determine that the blue hexagon is 1/3 the area of the outer hexagon.

This one is easiest of them all. Slide the blue hexagon down and to the left, where I have drawn in a red hexagon of the same size. This shows that the sides of the blue hexagon are ½ the sides of the outer hexagon, so the area of the blue hexagon is ¼ the area of the outer hexagon.

A little imagination solves the last problem. I have numbered the squares 1, 2, and 3. Now rotate square number 2 45°, and you see that square 2 is ½ the area of square 1, and square 3 is ½ the area of square 2 and therefore ¼ the area of square 1.

Quiz Question

This is from an Internet puzzle site, so don’t go searching for it on the Web. They posted it as an interactive game. You’re supposed to drag and drop the remaining numbers into the blank spaces inside the rings. Make the total inside each ring the same.

Post your answer as a comment below. You don’t have to show a picture. Just list the added numbers from left to right.

Quiz Question

Here’s another one I got off the Internet. Which goes to show I don’t make these up. Don’t go searching the Internet for the solution.

A number of regular pentagons and squares are arranged around the outside of a large blue regular polygon. Just the lower part of the arrangement is shown below.

How many sides does the large blue regular polygon have?

Post your answer as a comment below.

Update and solution

Use the fact that the exterior angles of a polynomial sum to 360°. That means the exterior angles of a regular pentagon are 360/5 = 72°. That means (see the top diagram) the exterior angles of the blue polygon are 90 – 72 = 18°. The exterior angles of blue polygon must total 360, so the blue polygon must have 20 sides.

Quiz Question

Each color in the above diagram represents a separate piece of a puzzle. Rearrange the pieces to form the figure below.

The images are to scale, so you can print the top one and cut the pieces apart to work the puzzle. Scan your solution and post the image as your solution. Use the comments section below.

Update and solution

Two people have proposed solutions. I printed the puzzle out and cut out the pieces. I was unable to solve it sitting at the breakfast table, I was when I went to the puzzle’s Web site and used their interactive controls to manipulate the pieces. Here is what I came up with.

Here is Helen’s solution.

Mike proposed a solution. See the comment below.

Quiz Question

This one is on the Internet, so no fair going to Google.

Three people are gathered in a room, and the puzzle master sticks a number on the forehead of each. Each can see the numbers on the foreheads of the other two, but nobody can see what’s on his own forehead. Here are the conditions of the three numbers, A, B, And C.

  • A + B = C
  • A > 0
  • B > 0
  • C > 0
  • All the numbers are different.

All there contestants are have perfect logic, and all know this fact and also the conditions stated above..

The puzzle master turns to person number 1 and says, “Look at the other two, and tell me what number is on your forehead.” Person 1 looks at the other two, and he sees 20 on one and 30 on the other. He says he is unable.

Same for person 2. He is unable.

Same for person 3. He is unable.

The puzzle master returns to  person 1. He announces what number he has on his forehead. What is that number? Post your answer in the comments section below.

Quiz Question

Here we see a prism, for the sake of this problem let’s call it a cereal box lying flat on a table. The height of the box (lying flat) is 12 cm. The other two dimensions are 25 and 36 cm. An ant at A wants to take the shortest path to B. The ant is not allowed to crawl along the bottom of the box. How long  is the shortest path?

Post your answer in the comments section  below.

Quiz Question

Number 150 of a continuing series

This is one I got off the Internet. I left the copyright information in the image, but readers are cautioned against using that to hunt down the solution. Work this one out for yourself and post your answer in the comments section.

There are nine combinations of colored cubes pictured above. When rotated properly, two of the nine are the same. Which two are the same?

Quiz Question

Number 149 of a continuing series

Here’s one from a site on the Internet, and I’m not going to tell you what site. You need to solve this one without help.

Use the numerals 1, 9, 9 and 6 exactly in that order to make the following numbers: 28, 32, 35, 38, 72, 73, 76, 77, 100 and 1000.
You can use the mathematical symbols +, -, ×, /, √, ^ (exponent symbol) and brackets.
Example: 1×9+9×6 = 63

Post your answer in the comments section.

Quiz Question

Number 144 of a continuing series

Here is another Mensa puzzle. I ripped it right out of my copy of American Way magazine on my way to some place I had never been. The caption in the magazine says, “Supply the missing number.” I’m going to be more explicit.

The implication is that each letter A – D stands for a different number (integer). Figure out which integer each letter stands for and supply the number that goes in place of the question mark. The solution is in  the magazine, and you can still track it down. Don’t do that. Supply your answer in the comment section below.