Markov Chain in Every Day Life

The picture shows a subway map.  A team of inspectors verifies passengers’ tickets at a station on a line, or all lines through it if there are many lines.  Then they randomly choose the next neighboring station and move there to make their inspection.

Subway map

How many times higher is the probability of being inspected at station C than at station A?

Are you eager to know the answer? Try yourself before reading how Markov Chain helps to solve the problem. The answer is here.

 

 

The perfect explanation is given in the PBS Infinite Series video:

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Cat, Rat, Hat, and Mat

 

 

Mary has a cat, and a rat, and a hat, and a mat.

If the cat is on the mat, and rat is in the hat, but the hat is on the mat, where is the rat?

This is a simple puzzle asked by Leslie Green, who collects dozens challenging puzzles.  The collection of Leslie Logic and Math Puzzles is presented at the website Aplusclick. It’s worth to try the challenging questions.

Selfie Math

Jim is going on a tour around the world. He has 5 tops, 4 bottoms, and 3 pairs of footwear. He wants to post a selfie everyday to show different places and his different outfits to his girl-friend Mary, who stays at home. He does not want to wear the same outfit twice. ## For how many days does he have enough clothing?

Leslie Green gives the answer : 96 days.

Can you explain why it is 96? What is logic behind?

 

 

The logic puzzle almost everyone gets wrong

This is a very famous logic problem:

“Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?

• A: Yes
  
• B: No
  
• C: Cannot be determined”

According to the Keith E. Stanovich in Scientific American more than 80 percent of people choose C, which is not the correct answer. The correct answer is A. Why?

This is another example of a similar problem:

There are only two handshakes in a meeting: John shakes hands with a person, this person shakes hands with Anna. Does a man shake hands with a woman in the meeting?

Answer

Mathematically Correct Way to Cut a Cake

What is wrong with cutting a cake? We always do it in a wrong way. What is better way? Alex Bellos gives the answer.

Geek’s Questions: The Art of Asking Yourself

A+Click contributor Gerry Geek just published a new true story: 

A group of friends visit me. They eat and drink everything, even the cat’s food, and then leave. The fridge is empty – only a glass of milk is left. I give half of the milk to my cat Ben. He drinks half of it and then I drink half of what is left. Again, he drinks half of what is left and then I do the same. We continue until nothing is left. What proportion of the initial amount of milk did I drink in total?

I remember the moment when I saw Jane for the first time. We were sitting at the same table at a tea room along with Mary and John. We looked at each other and I was sure that everybody immediately chooses another. If two boys and two girls choose a partner, then what is the probability that everybody chooses the person who chooses them?

Before I met Jane I had a relationship with three girls who lived in the same house. I sent three letters to them. If the postman put the letters into three different boxes without looking at the name of the recipient, what would be the probability that all girls received their letters?

The man who counted

The man who counted

“In 1932 Malba Tahan published what would became one of the most successful books ever written in Brazil – O Homem que Calculava – The Man Who Counted.”