thnik again!

We will return Monday May 2.

A beautiful mind.

Mathematics and visual arts intersect in the concept of symmetry. In art, symmetry is a basic design element, something that many people consider to be aesthetically pleasing. In math, symmetry can be defined and verified by finding motions that leave a design’s appearance unchanged. These motions can be combined and analyzed in much the way numbers are.

Play with symmetry here and watch a video that starts with a gun shot here.

The video has an interesting quote from a book whose title tickles my curiosity.

- They tell me it was kind of wild last night!?
- Well, I can tell you this. It didn’t go as planned.
- What actually happened?
- We were sitting in my garden having a wonderful supper.
- Were you sitting in 8 rows and 8 columns as usual?
- Of course! I always invite 63 people. Well, anyway, instead of sitting some people got up and walked around.
- In the middle of the meal?
- In the middle of the meal.
- What did you do?
- Well, I couldn’t just ask them all to sit down.
- Why not?
- So I turned it into an intellectual game.
- You did what?!
- I asked any in a 3×3 block or 4×4 block to sit if they were standing and stand if they were sitting.
- How did you choose the blocks?
- My intention was to choose them so after a while everyone would be sitting.
- How did it go?
- Not very well. The guests started to leave after they had been ordered to sit, stand, sit, stand, sit, stand a few times.
- How rude of them!
- Good guests sit on chairs.

Problem source: The USSR Olympiad Problem Book: Selected Problems and Theorems of Elementary Mathematics (452 pages, 3rd revised ed, 1993) by D O Shklarsky, N N Chentzov and I M Yaglom, via Delightful Puzzles.

If you take responsibility for yourself you will develop a hunger to accomplish your dreams. – Les Brown

A few days ago the topic was independent events. A and B are independent if the probability of A given B equals the probability of A. In fancy notation:

The problem was: There are eight cards numbered 1-8. The event A is drawing a card numbered 1, 2, 3, or 4, while B is drawing 3, 4, 7, or 8. Are the two events independent?

Inspired by this Mike commented: “Now, for more fun, find another event, C, which is mutually independent of both A and B.”

While Richard uttered: “For even more fun, find events A, B, C each of which is independent of the other two, even though the events as a threesome are not independent. (You don’t even need as many as 8 cards for this one.)”

Nobody took up the challenges. That is, till now…

I cry out for order and find it only in art. - Helen Hayes

When I was a kid I saw a quiz program on TV where the participants were allowed to use encyclopedias to find the answer. That meant that the questions were far from easy!

Google has used the idea to create “A Google a Day” where, of course, a Google search is recommended to find the unique answer.

To keep the game interesting for everyone, we created Deja Google – A wormhole inspired time machine that searches the Internet as it existed before the game began. Because nobody wants someone’s recent blog post about finding an answer spoiling their fun.

Here is an example:

My name is Robert. One day before my brother Rohan’s 19th birthday, our father had an album on the Billboard 200. Name the album.

And here is my own invention:

Taught in Trattenbach and worked in Skjolden. When did his mother and father get married?

Please make your own and post them in the comment section.

Man is the animal that draws lines which he himself then stumbles over. – Piet Hein

Click the image for a bigger, undistorted, version.