Taking the easy road this week. I pulled this week’s Quiz Question from an Internet site, so don’t go searching math puzzles on Google. Copied and pasted from the site:
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: 63 = 1×9+9×6
Post your answer in the comments section below. The winner will be whoever posts the greatest number of correct solutions.
This is from somebody else. It showed up on my Facebook feed just in time, when I needed inspiration for a new Quiz Question. It’s easy. Give yourself about 15 seconds. The problem was posed as:
There are three boxes and three statements. There is a car in only one of the boxes. Only one statement is true. Which statement is true, and in which box is the car?
Post your answer as a comment below.
Got this one from the Internet, so no fair going to Google for the answer.
ABCDEF × 3 = BCDEFA
Substitute a digit for each letter to provide the correct equation. Post your answer as a comment below. The solution will be provided next week (or sooner).
No solution given yet. I have not taken the time to solve this, but here are some hints.
Note that A < 4 and A ≠ 0. A ≠ 0 is not stated in the problem, but I’m taking it as assumed. If A > 3, then multiplying by three would produce overflow and a number with more digits.
BCDEFA is divisible by 3, which means ABCDEF is divisible by 3, since both have the same digital root.
BCDEFA is divisible by 9.
That should get people going, so I’m going to give more time to come up with an answer.
Easy one for a change, so give yourself 10 seconds to work it. It’s a single water hose with the ends uncoupled. Where are the ends?
Post your answer in the comment section below.
Update and solution
The solution is straight-forward. See the revised picture below.
Draw circles (ellipses) around A and B. Each has three hoses crossing into (or out of) the ellipse. Therefore, there must be a hose end within each of the two ellipses. Since there are only two ends (one hose), the ends must be under A and B. You don’t need to examine C and D, but if you do you will observe an even number of crossings.
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.
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:
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.
Another safe geometry problem. I find these on the Internet, so there’s not a lot of originality going to waste. Slice the picture into 2 sections from which you could make an 8×8 square.
Post your solution in the comments section below.
Mathematics again. What is the value of the indicated angle? Post your answer as a comment below.
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:
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.
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.
A number of people have posted responses, so I am going to supply the answer. See the following diagram:
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.
The squares are equal in size. What is A + B + C?
Post your answer as a comment below. Hint, it’s not all that hard.
One of a continuing series
Back to some basic math for a change. What is the answer?
Those aren’t radio buttons. You have to enter your answer as a comment below.