# Quiz Question

### Number 143 of a continuing series

#### I’ve been riding on airplanes again, and I lifted this problem from the American Way magazine, courtesy of Mensa.

This isn’t a geometry puzzle. It’s a problem in mathematical logic. There is a simple logic used for the first three triangles to determine the number on the inside by applying the logic to the numbers at the vertices. Use that same logic for the fourth triangle to determine the missing number inside the triangle.

## Update and solution

Yes, this really was a hard one. What you had to do was to figure out the logic that was consistent with the first three triangles. And not just any logic, but the simplest logic. And that simple logic is:

1. Ignore the number at the top and left vertices of the triangle.
2. Multiply the number at the right vertex by 6 to get the number in the middle.

The answer is, of course, 48.

# Quiz Question

### Number 142 of a continuing series

Here is another one courtesy of the Internet. See the diagram. The rectangles are identical (congruent). The perimeter of each rectangle is 222. What is the perimeter of the assembly shown above? Post your answer as a comment below.

## Update and solution

This one turned out to be so easy, I’m posting the solution today. Also, I have some spare time right now waiting for Barbara Jean, and I need something to do. Here’s a helpful diagram.

It is obvious you can transform the puzzle into the form shown at the top of the above three—without altering the perimeter. Similarly for the second of the above three. Now add the piece as I have done above, and the perimeter of the resulting figure is still the same.

Each rectangle in the puzzle is h×w, height and width. The perimeter is 6h + 6w or 3 times the perimeter of a single rectangle. The answer is 666.

# Quiz Question

### Number 141 of a continuing series

Here is one I found on the Internet. Not much explanation was given, but I am going to assume: the numbers are the areas of the small triangles. What is the area of the remaining triangle? Post your answer as a comment below.

## Update and solution

This was an easy one. To make it convenient to visualize, I have redrawn the figure above, not exactly to scale, but you should get the idea.

First I rotated the figure so the obvious line is horizontal. Now we see the problem as it is. Triangles 1 and 2 have the same altitude, h. Triangles 3 and ? have the same altitude H. Since triangle has an area of 2, its base must be twice the base of triangle 1. That means the base of triangle ? is twice the base of triangle 3. Since triangles 3 and ? have the same altitude, the area of triangle ? must be twice the area of triangle 3.

# Quiz Question

### Number 140 of a continuing series

Here’s another one for you frequent fliers. It’s from a copy of American Way and contributed by Mensa:

Here are six words:

• TWIN
• CHIME
• SCORE
• PLATE
• CARE
• HAT

Which of the six is least like the others. The difference has nothing to do with letters or syllables. Post your answer as a comment below.

# Quiz Question

### One of a continuing series

If you have ridden on an airplane recently, then you possibly already know this one. It’s from the Mensa quiz in American Way magazine.

Rearrange the letters in the word DOMINATION to form another English word. Post your answer as a comment below.

## Update and solution

This might look difficult at first, and you do need to apply a healthy vocabulary. However, you can use an approach that gets the process going. Look at the clue word. It ends in “tion.” which a lot of English words do. A good start is to presume the solution also ends in “tion.” Then solve using the remaining letters, and soon you come to “ADMONITION.”

# Quiz Question

### One of a continuing series

It’s another I stole off the Internet. No fair searching for the solution.

Here are two spirals. One figure is a single blue line. The other is two blue lines. Use your eyes only—no tracing with a pencil—which one is the single line?

# Quiz Question

### One of a continuing series

This is a famous Martin Gardner puzzle. If you’re a Gardner fan, then you already know this one. Anyhow, it’s easy.

Above is a chess board. Two black squares have been removed. The task is you have dominoes, each piece being the size of two squares. Is it possible to place 31 dominoes on  the remaining squares in the chess board?

# Quiz Question

### One of a continuing series

Here’s one I cribbed from the Internet. It’s out there, so don’t search it out for the answer.

A group of four people has to cross a bridge. It is dark, and they have to light the path with a flashlight. No more than two people can cross the bridge simultaneously, and the group has only one flashlight. It takes different time for the people in the group to cross the bridge:

• Annie crosses the bridge in 1 minute.
• Bob crosses the bridge in 2 minutes.
• Volodia Mitlin crosses the bridge in 5 minutes.
• Dorothy crosses the bridge in 10 minutes.

How can the group cross the bridge in 17 minutes? Post your answer as a comment below.

# Quiz Question

### One of a continuing series

Continuing into the new year, here are two easy geometry problems.

# Quiz Question

### One of a continuing series

A break from geometry problems on this, the first day of 2018. Here is a short geography quiz. Following is a list of American cities, in pairs. Your job is to, for each pair, pick the city with the largest population. Some of these are easy, others not so much so. After you finish picking, post your answers in the comments section and then grade yourself by going to Wikipedia. Use the population figures from the city’s Wikipedia entry. Some cities have the same name as others in other states. Assume the most prominent in case of conflict.

1. Dallas – San Diego
2. Austin – San Francisco
4. Houston – Boston
5. Muleshoe – Lipan (both in Texas)
6. Santa Fe – Denver
7. Kansas City (Kansas and Missouri)
8. Topeka – Memphis
9. Minneapolis – Fort Worth
10. Miami – Phoenix
11. Oklahoma City – Baltimore

1. Yes, San Diego is more populous than Dallas. Just barely. That’s one I missed.
2. In the rankings, Austin is number 11, San Francisco is number 14.
4. Houston 4, Boston 21.
5. This is an easy one. Muleshoe, Texas is much larger than Lipan.
6. Denver is number 23, Santa Fe does not make the top 100.
7. Kansas City, Missouri, ranks number 37. Kansas City, Kansas, does not make the list.
8. Memphis is number 20, larger than Boston. Topeka does not make the list.
9. Fort Worth, 17, is way ahead of Minneapolis
10. Phoenix, at number 6, far out-ranks Miami.
11. Baltimore 26, Oklahoma City 29.

# Quiz Question

### One of a continuing series

Merry Christmas. Here is an easy one. Make the usual assumptions from the drawing. What is the value of x? Post your answer as a comment below.

## Update and solution

I expected somebody would solve this quickly, and Mike nailed it within hours of posting. Mike only provided the solution. See the comment below. Here is how it unravels. See the image.

Obviously this is a semicircle and a square with a line tangent to the circle. We now have a right triangle ABC, tangent to the circle at D.

From  basic geometry we know that DB = 2. Also x = EA = AD. From there everything falls out quickly.

AB2 =AC2 + CB2

(x + 2)2 = (2 – x)2 + 4

x = ½

# Quiz Question

### One of a continuing series

See the image. The circles are radius 2.5 and 1.5. What is the area of the red section?

# Quiz Question

### One of a continuing series

A

B

Two photos of the moon, taken from my house in San Antonio, Texas, two nights apart. Which photo was taken first?

No fair running to an astronomy book. No fair going outside to look at the moon. Post your answer as a comment below.

Anybody who’s spent a lot of time outdoors knows this. In the northern hemisphere, especially as far as 30° north looks up at the moon from the north. That means the terminator, the significant aspect of moon phases, moves from right to left day after day. That means that photo B was taken before photo A. In this case two days before.

# Quiz Question

### One of a continuing series

Just when you thought we were finished with the math questions. This is from the Internet, so no  fair running to Google for an answer.

The red right triangle is circumscribed by the large circle. The two sides of the triangle are diameters of the smaller circles. Prove the blue area is equal to the red area.

# Quiz Question

### One of a continuing series

Keeping with a run of math questions… This problem is on the Internet. You have to provide an answer without going to the Internet.

The large arc is centered at O, The small arc is centered at D. Prove the two shaded areas are equal.

## Update and solution

Mike and Steve have provided correct solutions. See the comments. Steve worked out the math, and Mike stated the path to resolution rather cryptically. Both invoked π, which is not necessary. Try this approach.

The triangle is a right, equilateral triangle. The hypotenuse is √2 times the base and is also the diameter of the small semicircle. You will have no problem from that point concluding the small semicircle’s area is ½ the area of the large semicircle. The area A of the small semicircle is equal to the area of the triangle + the circle segment subtended by the triangle’s hypotenuse. The area of the triangle is A – the area of the segment. The area of the lune outside the large semicircle is A – the area of the segment. Therefore the two areas are the same.

# Quiz Question

### One of a continuing series

Back to math questions for a change. Full disclosure: I don’t make up all of these. This is from an Internet site. No fair going to the Internet to get the answer.

The triangle is equilateral. Prove the shaded area is equal to the inner circle. Post your answer as a comment below.

## Update and solution

Mike is the first and only to provide the correct solution. A reasoning goes like this.

It is easy to demonstrate (exercise left to the reader) that the inner circle is ¼ the area of the outer circle. Then the region between the inner and outer circles is ¾ the area of the outer circle. The blue-shaded regions total 1/3 of this difference or ¼ the area of the outer circle. The inner circle is equal to the blue-shaded area.

# Quiz Question

### One of a continuing series

More fun with word games…

37 years ago I was taking a course in database design, and the professor got onto the subject of data security. He discussed how contents of a file could be encrypted to protect your information from prying eyes. To illustrate, he wrote two lines of text on the board:

FRSRXRMG

Then he turned to the class, pointed to the board, and asked, “What is this?”

I had been watching as he was writing and had started running some stuff through my head.

“Anybody?” the professor inquired.

I raised my hand.

He said, “Yes?”

I said, “Well the top one is a …,” and here I inserted an encryption technique. “And the second one is …,” and I mentioned another method.

The professor looked a little unsettled. “But what do these mean?”

So I told him.

Today’s question (problem) is, translate the two lines of text. Post your answer as a comment below. I will post a hint tomorrow if nobody has the solution by then.

Greg got it right. I was looking at the words. What had about that many letters? What course was I sitting in? Database Design. Bingo. Then my cruel nature emerged. The professor asked how I did that. I told him I had experience with that sort of thing, and I didn’t say any more.

## Another update and correction

Mike has pointed out the obvious. The top line of text has an extra B. My bad. I scanned this line not enough times to spot the error. I apologize for posing a Quiz Question with no answer. Here are the two lines of text that make sense.

FRSRXRMG

# Quiz Question

### One of a continuing series

American Airline frequent fliers already know this one. Here are the letters:

### BBELRU

List the common English words that can be formed using all of the letters once in the word? Post your answer as a comment below.

# Quiz Question

### One of a continuing series

Airliner crosses Vineland Avenue North Hollywood while landing at Burbank Airport

### This is the kind of question that sometimes comes up in engineering.

An engineer is tasked with designing a new airplane, with two requirements. The airplane must be able to carry 8 passengers, and the design must use engine model A3-28, made by the boss’s company.

The engineer completes a design, and then does some calculations. The plane will not fly with a single engine of that model, but it will fly with two engines. The engineer’s boss tells him to modify the design and use two of the engines.

The engineer knows this is a bad idea.

Why?