thnik again!

- 197 is a fascinating number!
- How come? No, don’t tell me! Let me guess.
- I am all ears.
- Because it is the smallest number that gives only one result when you search for it on Google.
- Not even close. But that is a fascinating thought.
- What is?
- The problem you just mentioned.
- You mean, what is the smallest number that gives only one hit in a Google search.
- How would you find out?
- That’s what makes it so fascinating. I have no idea!

A chess game is divided into three stages: the first, when you hope you have the advantage, the second when you believe you have an advantage, and the third… when you know you’re going to lose! - Savielly Tartakover

- Start with the numbers 1, 2, 3, and 4.
- What do I do with them?
- Add them up, that’s what you do with them.
- That is easy. I get 9.
- Try again.
- Did I say 9? It was a slip of tongue, I meant 10.
- Now you have five numbers, 1, 2, 3, 4, and 10.
- I feel rich!
- Pick any four of them and add them.
- Why on earth would I do that?
- To get a bigger number, you silly.
- What is the aim?
- It may stop the rain.
- Seriously, what are you getting at?
- Continue like that. Pick any four numbers amongst the numbers you already have to create a new number. The question is, can you ever reach 1000?
- I have a feeling that it is clearing up already.

Problem source: Wisconsin Mathematics, Science and Engineering Talent Search.

The greatest advantage in gambling lies in not playing at all. - Gerolamo Cardano

- What on earth are you wearing?
- It is a T-shirt I bought in Cairo on my last holiday.
- T-shirt with math on it! Only you would be crazy enough to pay for something like that.
- I didn’t. I got it for free.
- How come?
- It was free for those who could prove that the equation has no solution when the xs are odd integers.
- And that you call a holiday?!
- Actually, it gets better.
- Do explain.
- I got another one for free as well.
- Of the same kind?
- I proved that there is a solution when the xs are distinct positive integers.
- Do you mind if I open the window?

Problem source: Math problems from PIMS.

What is the Secret of SUCCESS….? ”RIGHT DECISIONS”.

How do you make Right Decisions…? ”EXPERIENCE”.

How do you get Experience….? ”WRONG DECISIONS”

- Dr. Abdul Kalam

I like to think that my thinking sometimes is refined, or of the higher order. In the valuable blog ”CASTLE - Great Blogs for Busy Administrators” via Scott McLeod, I found this quote from Education and Learning to Think.

Before you read the list, what do you believe are the characteristics of higher order thinking?

Higher order thinking is nonalgorithmic. That is, the path of action is not fully specified in advance.

Higher order thinking tends to be complex. The total path is not “visible” (mentally speaking) from any single vantage point.

Higher order thinking often yields multiple solutions, each with costs and benefits, rather than unique solutions.

Higher order thinking involves nuanced judgment and interpretation.

Higher order thinking involves the application of multiple criteria, which sometimes conflict with one another.

Higher order thinking often involves uncertainty. Not everything that bears on the task at hand is known.

Higher order thinking involves self-regulation of the thinking process. We do not recognize higher order thinking in an individual when someone else “calls the plays” at every step.

Higher order thinking involves imposing meaning, finding structure in apparent disorder.

Higher order thinking is effortful. There is considerable mental work involved in the kinds of elaborations and judgments required.

After having read the list I suddenly realise that many of the problems in think again! require higher order thinking. I especially like the words ‘conflict’, ‘interpretation’, ‘disorder’, and ‘judgement.

By clicking on the ponies you are going to make them equal. Or, as they say on the site “Make the ponies prance!”

I got them to face the same way, but they were not of the same size, so I failed. Don’t let that happen to you!

My neighbour invited me over to supper the other night. She covered the square table we were eating at with three 1m x 1m table cloths. That made me think. What is the largest square table that can be covered with three 1-meter squares?

Problem source: Dan’s problems.

It is better to have a permanent income than to be fascinating. - Oscar Wilde