think again!

Problem source: Columbus State University’s math contest.

- Did you get the Go board you ordered on the Internet?
- You mean the rectangular wooden block I mentioned on the phone?
- The very same.
- Yes, it arrived last week.
- Good.
- Go-ban it is called. It came with four legs I will attach to the block.
- How big is the block?
- Its width, height, and length are all different.
- How exciting!
- And they are alle prime numbers when measured in cm.
- So what are its dimensions?
- Its volume is a three digit number and its total surface area is a four digit number. 

Problem source: Problem of the Week.

Fat Mona Lisa by Fernando Botero.

- So the answer is 0.2?
- Well, not exactly.
- What do you mean?
- I rounded the answer to two decimal places and  the number I then got I rounded to one decimal place.
- Why on earth did you do that?
- Because I can’t afford a ticket to the moon.
- Try to be serious.
- That’s the way my grand mother taught me.
- And what was your original answer?
- I don’t know. But it is likely that it was between 0.15 and 0.25.
- How likely?

Problem source: MathsChallenge.net.

- Do you know what a prime number is?
- A number that is more important than other numbers.
- Why do you say that?
- The prime minister is the most important minister and when I was in my prime I felt very important.
- I see.
- For me 1, 3, and 4 are the only primes.
- Please share!
- My children are one and three years old and I have four dogs.
- What about yourself?
- I am odd.
- No comment! In school prime numbers are defined as those that have exactly two divisors, 1 and themselves.
- You mean 2, 3, 5, 7, 11, 13, …?
- Exactly!
- Here is a challenge for you. Find the prime number less than thousand that is the sum of the most consecutive primes.
- I need a hint.
- 41 is a prime and 2 + 3 + 5 + 7 + 11 + 13 = 41. It is the prime number less than hundred that is the sum of the most consecutive primes.
- I understand. May I use a computer to help me?
- Be my guest.

Problem source: Project Euler.

- Where I live clotheslines are prohibited!
- By whom?
- It is one of the strata rules.
- And why is it illegal to dry clothes in the sun?
- I am not sure.
- Could it be because it is the most ecological way to do it?
- Someone told me that it would lower the property values.
- How come?
- I don’t remember very well, but I do recall that somehow the slums in Hong Kong is involved.
- You mean if a butterfly flaps it wings in a slum it may effect the weather and therefore the property values.
- Something of the sort.
- Talking about clotheslines. I have made a discovery!
- Really?
- Most people hang their clothes along the lines as in the image above.
- Isn’t that the only way?
- That is my discovery! A few people hang the clothes between the lines instead of along them.
- May I have a drawing?
- Sure thing!

- Here are seven horisontal clotheslines, ab to op. Normally people hang clothes using these lines. However, instead one may hang the clothes between the lines, i.e. along the lines ab to kl in the drawing on the right.
- And you are saying that one may fit more clothes using the vertical lines than the horisontal ones?
- That is my discovery!
- You surprise me! I didn’t know you could be creative at all.
- May I make a confession?
- I saw this in Southern Spain two months ago.
- So you didn’t invent it?
- That’s correct. I did like Columbus. As you may know he didn’t invent America. 
- So who invented it?
- I have no idea.

- 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?

- 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?

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.

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?

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.