thnik again!

Match pairs of images that are not obstructed by other images. Play Connect2 here.

Two thieves steal a necklace made of diamonds and rubies. The necklace has an even number of diamonds and an even number of rubies evenly spaced out.

They decide to cut the necklace in half in order to share it fairly, but are unsuccessful. How were the diamonds and rubies positioned?

Problem source: wu forums.

If all the world’s a stage, I want to operate the trap door. - Paul Beatty

- Can you put some tiles in my garden, please?
- Can do. Which colours are they?
- Some are black and some are white.
- What pattern do you have in mind?
- The tiles will make a straight walkway only one tile wide.
- And the pattern?
- I don’t care. But I do have one condition.
- One moment. Let me write it down.
- Put the tiles down in such a way that there are at least two tiles of the same colour and the tile midway between them has the same colour too.
- Is this a prank call?
- Do you mean it can’t be done?
- No, it is just too easy. Three white tiles in a row will do.
- I see. I am sorry, I guess I explained it badly. I want you to put the tiles down in a random fashion.
- You mean we should throw a coin to decide if the next tile should be black or white?
- Yes. 
- We can do that, but what is your problem?
- Will I be guaranteed to get two tiles of the same colour with the tile midway between them of the same colour too?
- That is a different question. I will switch you over to Mr. Knowles. He knows more about this. Just one minute.

When ideas fail, words come in very handy. - Johann Wolfgang von Goethe

- How are your apples these days?
- Just fine, thank you. Why do you ask?
- No, no reason. I just came to remember that you have quite a few apple trees.
- I have exactly 20,001 x 20,001 – 1, or 400,040,000 in all.
- How do you know the exact number? Do you count them every day?
- I have put the trees in a square grid with my house in the center.
- Please explain.
- To the left of my house I have a row of 10,000 trees, equally spaced out with ten metres between them.
- And to the right?
- The same. And the same above and below the house.
- Do you grow trees in the sky?
- Very funny.
- And I assume you have trees in rows and columns with ten metres between each row and between each column.
- As I said, they are in a square grid.
- Now I remember why I came to think of your apples.
- Tell me.
- How many of your trees are exactly 10,000 metres from the center of your house?
- I know of four, but I guess there may be more.
- How many more?

When we ask for advice, we are usually looking for an accomplice. - Marquis de la Grange

- How is your new diet going?
- It was going fine till last week. I lost weight, got stronger, and felt great.
- What happened last week?
- I read that Oat Bran is Satan’s fiber.
- Satan who?
- Joke if you must. For me it robbed the appetite.
- How come?
- I stumbled over this:

Satan has so blatantly encoded his word into the health-food craze, revealing the terrible hoax in an obvious manner. Seek the message implicit in the words, O-A-T and B-R-A-N. Oat bran is certainly the greatest force in the popularization of health food. And strangely enough (or not) there is a hidden meaning. If one adds up the numeric values of the letters (A=1, B=2, C=3…Z=26), the message becomes clear.

O(15) + A(1) + T(20) = 36

B(2) + R(18)+ A(1) +N(14) = 36

- What is wrong with 36?
- It is not thirty-six, it is three sixes, or 666. The Devil’s number. 
- And you take this nonsense seriously? 
- Why shouldn’t I?
- Beats me! By the way, you may like this clip from Newsweek:

Woody Allen cuts his banana into seven slices each morning. Six slices, or eight, and something bad might happen. “I know it would be total coincidence if I didn’t slice it into seven pieces, and my family were killed in a fire,” he says. “I understand that there could be no correlation, but, you know, the guilt would be too much for me to bear, so it’s easier for me to cut the stupid banana.” 

- Here is one that scares me even more than Oat Bran:

The worst superstition I had — and I’m told this is an Irish thing — is that I used to believe that worrying about something prevented it from happening. Conversely, if I didn’t worry about something, and it happened, it was my fault for not worrying. 

Technology is dominated by two types of people: those who understand what they do not manage, and those who manage what they do not understand. - Putt’s Law

- Emes is the Yiddish word for truth.
- I didn’t know that.
- Truth is hard to find.
- That I knew!
- Did you know that the digit sum of 441 is 9?
- 4 + 4 + 1 = 9. So what?
- Did you know that no matter what you multiply 36 with the answer’s repeated digit sum is 9?
- Let me try. 36 x 17 = 612 and 6 + 1 + 2 = 9. It works!
- Could have been a lucky coincidence, try another one.
- 36 x 1952 = 70272 and 7 + 0 + 2 + 7 + 2 = 18. It failed!
- 1 + 8 = 9. It worked!
- Is that what you meant when you said ‘repeated’ digit sum?
- I guess so.
- Let me try a last example. 36 x 9853 = 354708. 3 + 5 + 4 + 7 + 0 + 8 is 27 and 2+ 7 = 9. It always works!
- Can you prove it?
- I just did. I tried three numbers and they all worked.
- I see.
- I didn’t know I had it in me to be a mathematician.
- Neither did I.
- I feel great!
- By the way, did you know that 9 is the mispar katan of truth?
- Mispar who?