Quiz Question

One of a continuing series

mathematics-gemoetrydivideidentical

Readers have been getting off easy recently. I’m going back to geometry questions, so give your brain a work out.

I found this on the Internet, but you shouldn’t go looking for the solution without first coming up with a solution. With a single line, does not need to be straight, divide the shape shown above into two identical parts. Post your answer as a comment below.

Actually, send me a copy of your solution by email, and I will post it.

Update

No solution. I have not solved it. Mike proposed a solution. See his comment below. Unable to post a graphic, he indicated the shape of the solution as follows:

XX
XXX
X

See the figure below:

Shape A is the original, turned upright. Shape B is Mike’s proposed solution in graphical form. My apologies if I misinterpreted Mike’s rendition.

What is apparent to me is that shape B cannot be fitted twice into shape A. I’m calling the Quiz Question still  unanswered.

Quiz Question

One of a continuing series

mathematicscomputeangle

Mathematics again. What is the value of the indicated angle? Post your answer as a comment below.

Update

Three people have submitted correct answers, all holding Ph.D. degrees, but none in mathematics. Here is my solution, which I believe to be the simplest approach. See the diagram:

mathematicscomputeangle-02

It’s the same as the original diagram, but I have added some labels, and I have added line BC.

Notice immediately that BC is the same as AB. If you don’t notice this immediately, then stop reading now and get into another line of work. Now notice that angle BAD is the same as angle EBC. Again, if you don’t notice, stop reading. BAD = EBC implies ABC is a right angle. Again, you can quit while you’re ahead. We have a right isosceles triangle, which means that BAC is 45°. And no mental gymnastics have been required.

Quiz Question

One of a continuing series

math-angleproblem

This popped up on my Facebook time line, posted by somebody else. So I stole it, and here it is: What is the sum of all the blue angles? Post your answer as a comment below.

Update

A number of people have posted responses, so I am going to supply the answer. See the following diagram:

math-polygonangles

What is the sum of interior angles of a polygon? The example of a triangle explains. The triangle is ABC, defined by its three interior angles. But concentrate on the complementary angles a and b and c. What is the sum of those angles? Consider the line ab. Line bc branches off from ab with a change of direction equal to angle b. Follow the path around the triangle, and the total change of direction is 360 degrees. That’s going to be the total of a and b and c. The sum of a and A is 180° so the sum of all angles is 3 × 180 = 540. 540 – 360 = 180, the sum of interior angles of all triangles.

The method holds true for all polygons. The polygon in this puzzle is unusual in that the path makes two complete turns or 360 × 2 = 720. There are 6 sides and six interior angles, so the sum of the interior angles is 6 × 180 – 720 = 360.

Quiz Question

One of a continuing series

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This is going to be very easy for most. Some will trip up on it.

There are three closed boxes. One box has only apples. One has only bananas. One has a mixture of apples and bananas. Each box is labeled to identify the contents. The problem is, all the labels are wrong. You are allowed to peek inside one box and are required to determine the contents of the two remaining boxes. Which box do you open and look into?

Stop

If you have gotten to this point you have gone too far. You should not have to think about this problem to solve it. Just post your answer in the comments section below. And also tell everybody why this didn’t require working through the possibilities to come up with the correct answer.

Quiz Question

One of a continuing series

mathematics-numbers-01

This week’s Quiz Question should be easy. Easy for those who stayed awake in class. As I understood it, this was explained once and then never again.

Myriad is a number. What number? How much is a myriad?

You can look this up on the Internet, but don’t. Enter your answer as a comment below.

Update

Greg wins. His is the correct answer. A myriad is 10,000. How this name came about, I do not know. It’s time to look it up:

myriad (n.) 1550s, from Middle French myriade and directly from Late Latin myrias (genitive myriadis) “ten thousand,” from Greek myrias (genitive myriados) “a number of ten thousand, countless numbers,” from myrios (plural myrioi) “innumerable, countless, infinite; boundless,” as a definite number, “ten thousand”

Greg was paying attention in grade school.

Quiz Question

One of a continuing series

mathematics-numbers-01

I stole this from somebody else:

Continue the following number series with the group of numbers below which best continues the series?

1 10 3 9 5 8 7 7 9 6 ? ?

11 5
10 5
10 4
11 6

Provide your answer in the comments section.

Update and Answer

Take a look at the sequence. The first number and every second thereafter increases by 1. The second number, and every second thereafter decreases by two. Therefore the next two number in the sequence are 10 and 4.

Update and Correction

Actually, I got it backward. It’s the odd numbers that increase by 2, and it’s the even numbers that decrease by 1.