What are the odds of three generations of the same family all having boys born on the same day?
According to this article the odds are 272,910 to one. Do you agree?
Problem kindly submitted by John Shonder.
And remember, no matter where you go, there you are. - Earl Mac Rauch
- Do you know the natural numbers?
- You mean 1, 2, 3, …?
- Exactly. I have been studying them lately.
- You are still unemployed?
- Here are my three discoveries.
- Shoot.
- They are in the form of puzzles.
- I didn’t expect anything else.
- Find the three smallest odd numbers that are not the sum of two primes.
- 9 is 7 + 2 so that is not one of them.
- You are a genius!
- !
- Find the three smallest even numbers that are not the sum of two primes.
- 4 is 2 + 2 so that is not one of them.
- You are a genius squared!
- What is the third discovery?
- What does the guy in the image above have to do with all this?
I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers. – Georg Cantor
She made the top-ten list, but who is she?
If you were to pick the ten greatest mathematician, alive or dead, who would you pick? How many would be alive? How many would be women?
Think about it and then have a look at Alex Bellos’ selection here.
Update:
A BBC documentary on Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing.
You have a grid of squares, some light and some dark. Your aim is to light all the squares up at the same time. You can choose any square and flip its state from light to dark or dark to light, but when you do so, other squares around it change state as well.
Each square contains a small diagram showing which other squares change when you flip it.
- You never talk about your time in the military!
- Do you want me to?
- Of course.
- OK. Once we were 100 men in a unit, and every evening three of us were on duty.
- Did it ever happen that after a certain period of time each soldier had shared duty with every other soldier exactly once?
- Why do you interrupt? Don’t you know it’s rude?!
Problem source: BAMO Problems.
A page of history is worth a volume of logic. - Oliver Wendell Holmes, Jr.
The answer to yesterday’s problem was that I was copying files on a Windows XP machine. First I was told it would take 5 minutes, a bit later I was told 28 minutes. It oscillated way too much to my liking. In the end it oscillated between 60 seconds and 5 seconds with some visits to 2 and 1 minutes.
I might understand the oscillation if I was downloading stuff from the Internet as Internet speed varies a lot, but I was copying from my hard disk to my memory stick with no other processes going on.
So, here is today’s challenge.
1. Explain why Microsoft couldn’t come up with a better algorithm to predict time remaining of copying files.
2. Suggest a better algorithm.
I am a student of learning. The classroom is my laboratory. – Jan Nordgreen