thnik again!

- My son will soon be three years old!
- That is great! How will you celebrate it?
- I thought of putting three lights on a cake.
- It is not original, but it is a good idea.
- The lights will be placed one behind the other in a straight line.
- OK. Any reason why on a line? 
- The middle light will be equally far away from the two other lights.
- Will it be a chocolate cake?
- The middle light is twice as high as the two other lights, but thinner. It can burn 4 hours.
- That should be enough. I mean, if your son really needs to take his time to blow it out.
- The other two can burn 4.5 and 9 hours.
- You are not going a bit over board with these lights?
- After a while the top of the three lights will make a straight line. Slanted, yes, but straight.
- When will that happen?
- I thought the one who could find out would get an extra piece of the cake.
- !!!
- What do you think? 
- Is ‘You’re crazy!’ an option?

A deaf ear is followed by death and an ear that listens is followed by blessings. - The Samburu people, Kenya

- The differences between people should never be underestimated.
- Right on!
- I am glad you agree.
- What about multiplying them?
- Multiplying what?
- Their differences.
- I am lost!
- Take three people aged 25, 7, and 84.
- OK.
- Their differences are 18, 77, and 59.
- Go on.
- 18 x 77 x 59 = 81774.
- So?
- You mean you don’t notice anything?
- Not a thing.
- The product is even!
- Probably just pure luck.
- I don’t think so. I have come to believe that the product of three people’s differences is always even.
- So what?
- Doesn’t it make you want to sing and dance?

Realism … has no more to do with reality than anything else. - Hob Broun

1/17  = .[0588235294117647]

10/17 = .[5882352941176470]           

15/17 = .[8823529411764705]

14/17 = .[8235294117647058]           

4/17  = .[2352941176470588]           

6/17  = .[3529411764705882]           

9/17  = .[5294117647058823]           

5/17  = .[2941176470588235]           

16/17 = .[9411764705882352]           

7/17  = .[4117647058823529]

2/17  = .[1176470588235294]           

3/17  = .[1764705882352941]          

13/17 = .[7647058823529411]           

11/17 = .[6470588235294117]           

8/17  = .[4705882352941176]           

12/17 = .[7058823529411764]

My neighbour has a kid who has a calculator that according to the kid gives strange results. The other day my neighbour showed me the pattern above and asked with pleading eyes: How do you explain it?

Suddenly I remembered I had an imaginary meeting I was already late for.

From the pages of The Math Less Traveled.

Computers are useless. They can only give you answers. – Pablo Picasso

In Surat Thani, Thailand, last week I met a coconut farmer with ten acres of land. He told me that each palm tree needs to be at least five meters from every other palm tree to grow as fast as possible. After only three years it will start to bear coconuts.

Later I was wondering how many palm trees he could have on his land. Obviously it would depend on the shape of the land, so I looked for the minimum and maximum number of trees.

What do you think?

What a blessing it would be if we could open and shut our ears as easily as we open and shut our eyes! - Georg Christoph Lichtenberg

A winter evening in Väinölänniemi.

Your aid I want, nine trees to plant

In rows just half a score;

And let there be in each row three.

Solve this: I ask no more.

From ‘Rational Amusements for Winter Evenings’ by John Jackson, 1821.

Say not, ‘I have found the truth,’ but rather, ‘I have found a truth.’ – Kahlil Gibran