 # Quiz Question

### Number 222 of a series The radius of the small circle is 1. What is the radius of the large circles (all the same)? # Quiz Question

### Number 221 of a series These are all squares with areas as marked. What is the area of the square with the question mark? Post your solution in the comments section below. # Quiz Question

### Number 220 of a series This is from a book titled 2nd Miscellany of Puzzles. The description in the book is circuitous, so I distilled it to the essentials, as I interpret the problem. A circle sits on a 2-D grid with the coordinates marked where the circle intersects the axes. What is the diameter of the circle? # Quiz Question

### Number 218 of a series I haven’t worked this one. It popped up on my Facebook feed while I was lolling about on vacation, and I captured this screen shot. Here are the instructions:

• There are three patterns.
• Two diagonal and one vertical
• What goes in the center box?
• It is not mathematical, per se.
• No partial answers. Explain all three patterns. # Quiz Question

### Number 217 of a series The image above is a cutout from a map of the United States. It shows only borders and no other details. Only portions of three states are shown. What state is shaded red?

## Update and Solution

Nobody got this one last week. The excerpt from Google Maps should be enough to resolve the question.  # Quiz Question

### Number 216 of a series I have a map of the united states showing only the outlines of the states. One state is colored in red. Here is a portion of that map. What state is colored in red. No fair going to a map. You need to answer this week’s Quiz Question from your personal knowledge. # Quiz Question

### Number 215 of a series I found this on the Internet. No fair going to Google for the answer.

Show that for any natural n, at least one of two numbers, n or n+1, can be represented in the following form: k + S(k) for a certain k, where S(k) is the sum of all digits in k. For instance, 21 = 15 + (5+1) # Quiz Question

### Number 214 of a series Here is a calendar. It could be any calendar. I drew a 3×3 box around 9 dates. What is the sum of the numbers in the box? You are allowed five seconds.

## Update and Solution

Mike has the right approach. To solve this in under five seconds you need to know about the life of Carl Friedrich Gauss. As a young school boy he was assigned the problem of adding up a column of large numbers. He noticed the professor wrote the column of numbers as an arithmetic series. He quickly realized the sum was the product of the average and the number of numbers. The average would be the middle number (odd number of numbers) or half way between the two middle numbers. He turned in his answer so quickly the professor was astounded.

Days in a month are an arithmetic sequence. All this problem does is to chop the sequence into three , equally spaced, sequences of the same length. The sum will be 9 times the middle number.

180 (in under 5 seconds) # Quiz Question

### Number 213 of a series I found this on the Internet, so no fair using Google.

Each of the lists below groups letters according to a certain rule. Your challenge is to find that rule and use it to determine where the X, Y, and Z would go.

List #1: A E F H I K L M N T V W

List #2: B C D G J O P Q R S U # Quiz Question

### Number 212 of a series The circles represent four pennies arranged in a square. All right, they don’t look like pennies, but use your imagination. Also use your imagination to move two pennies to form another square smaller than the original.

Post your solution in the comments section below.

## Update and Solution

Everybody who had a go at this one got it. Here’s the picture.  # Quiz Question

### Number 211 of a series What result do you get when you multiply all the digits on a phone keypad? Post your answer as a comment below.

## Update and Solution’

A trick question, to be sure, and several people provided the correct answer. The trick is based on people not remembering that one of the digits on a phone key pad is a zero. # Quiz Question

### Number 210 of a series Examine the numbers in the triangular formation and determine the values for E and D. Enter your answer in the comment section below.

## Update and Solution

Mike provided an answer in the comment below. Here’s what you need to do.

First notice that 198 + 263 – 15 = 446. Then take it from there. # Quiz Question

### Number 209 of a series What’s the last digit of the following?

## Update and Solution

Mike saw through this one early, only his comment was so cryptic I missed it. See below. I didn’t see it until I started working through it, then I thought, “too easy.” Here is how it works.

A is the last digit of 171999. B is the last digit of  111999. C is the last digit of 71999.

It is obvious A = C, so the answer is B. And B is 1. # Quiz Question

### Number 208 of a series What goes in place of the ? Submit your answer as a comment below.

It would appear I started this series four years ago.

## Update and Solution

Examine the problem. The first thing that becomes apparent… All right, maybe the second thing… is the following:

3 × 15 – 1 = 14

3 × 300 – 1 = 899

So I am guessing 3 × 150 – 1 = 449, the answer. # Quiz Question

### Number 207 of a series See the diagram above. What goes in place of the question mark? Submit your answer in the comments section below.

## Update and Solution Please note that in all cases ABC + D. # Quiz Question

### Number 206 of a series #### This one is from The Moscow Puzzles by Boris A. Kordemsky, page 44.

That’s supposed to be a chess board above, although I have not shaded in the black and white squares. It doesn’t matter, because this is not a real chess game. The black circles are black pawns, about twice as many as in a real chess game. The question is can you set a white knight on the board and proceed to capture all 16 pawns in 16 consecutive moves? Let’s assume you can, then what are the moves?

## Update and Solution

Mike comments this is too easy. Could be. Kordemsky has this to say:

Start by capturing one of the pawns not marked with a red dot in the diagram below. Then the rest should be straight-forward. # Quiz Question

### Number 205 of a series I’m late posting this week’s Quiz Question. Monday was a busy day. But here it is. I came across an item posted on the Internet—The Subtle Art of the Mathematical Conjecture. It has some interesting stuff, including proved and yet to be proved conjectures in mathematics. There is a discussion of Fermat’s Conjecture, and there is this:

Counterexamples can lie far ashore, like the one found by Noam Elkies, a mathematician at Harvard University, disproving Euler’s conjecture, a variation on Fermat’s conjecture that states that a fourth power can never be written as a sum of three other fourth powers. Who would have guessed that the first counterexample involved a number of 30 digits?*

The asterisk points to a note:

20,615,6734 = 2,682,4404 + 15,365,6394 + 18,796,7604.

Am I the only one who sees something wrong with this equation? Post your comments below.

## Update and solution

Mike and Elmo got this one right. I had it wrong. I tried to check the math in my head and miscounted the multiplications. Shit happens. # Quiz Question

### Number 204 of a series Math time again. Some time ago I had the idea to clear out shelf space, so I dumped all the copies of Schaum’s Outline books that are available on Kindle. This is from Schaum’s Vector Analysis, Chapter 2.

2.11. Show that the vectors A = − i + j, B = − ij – 2k, C = 2j + 2k form a right triangle.

i, j, and k are the unit vectors parallel to the 3D coordinate axes. To be clear, imagine each vector as a straight line oriented in space but movable. Can you move the three lines into position to form a right triangle? Give a mathematical proof.

The answer is in the book, but you know better than to look for the answer. Post your answer as a comment below.

## Update and solution

First it is needed to demonstrate the three vectors satisfy the Pythagorean Theorem. Square the lengths of all vectors and see if the sums of two add up to the third. So we have:

|A|² = 2

|B|² = 6

|C|² =8

That works.

To form a closed polygon (triangle) the sum of the vectors must be zero.

Sum = (-1 -1)i (1 -1 +2)j (-2 +2)k, which is not zero. But if you reverse A, then

Sum = (1 -1)i (-1 -1 +2)j (-2 +2)k, which is zero.

Also, note the dot product of A and B is zero. The two vectors are orthogonal.

So the three vectors form a right triangle. # Quiz Question

### Number 203 of a series

Here is something for those who paid attention in high school physics class. See the diagram below. This is a metal (wood, plastic, glass) tube. The end on the left is closed, while the end on the right is open. If you blow across the open end sound waves travel back and forth within the tube. The lowest frequency at which the air column in the tube vibrates is call the fundamental frequency of the tube. In this case the fundamental frequency is 420 Hz.

The tube below is the same length as the tube above, but the left end is open. Again when you blow across the open end on the right you get the air column vibrating. What is the fundamental frequency of the open tube? Why? Hint: wind musical instruments operate off this principle.

Post your responses in the comments section below. # Quiz Question

### Number 202 of a series Something for the math people. The plane shown above is defined by:

### z = 5x +4y

What is the unit vector perpendicular to the plane? Give the answer in terms of

### (ai, bj, ck)

Where i, j, and k are unit vectors for the x, y, and z axes. Submit your answer in the comments section below.