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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17 Best Puzzles of 2017

 

Aplusclcik team chose 17 Best Puzzles of 2017.

They are:

What country has the lowest birth rate in the World?

If certain words in this question are spelt wrong, how many of the eighteen words are spelt wrong?

A claustrophobic gentleman chooses his place in the train that will enter a tunnel just after the station. Where is the best place for him?

Read more at

17 Best Aplusclick Puzzles of 2017 from Igor Kokcharov, Ph.D, PMP

APLUSCLICK.ORG is online

To respond to growing demand of international users, we redirect http://www.aplusclick.com to the new free website www.aplusclick.org . All links  for extension .com are the same for extention .org  Now the site is hosted in Switzerland. Please update your links. Happy challenges at www.aplusclick.org

Mystic Number 7

Why we frequently use number 7?

Why there are seven days of week? seven deadly sins? seven wonders? . . . .

Look for the answer in the night sky or at aplusclick.org

Everyday Brain Training

Millions people do everyday physical training / exercises. They want to keep their body in good shape.

Why a smaller number of people intentionally do everyday brain training / exercises?

• The absence of intelligence is not so visible as defaults of the physical shape.
• Everybody thinks that he / she is enough smart.
• Playing computer games is considered as a mental work.
• No time, there are other priorities.
• Lack of motivation / self-discipline.
• There are not interesting intellectual challenges to meet everyday.
•  . . .

Many types of work, games, discussions concentrate on a limited types of challenges. You can play many hours everyday, but the types of exercises are limited: just kill / catch somebody, and you do it again and again.

Aplusclick tries to respond to the challenges by creating a collection of different logic puzzles for all ages. There are several thousands different types of problems. Enough to do everyday training for many months.  Many of them demands exceptional intelligence.

Do your everyday 5-minute brain training at the free website Aplusclick and keep your brain sharp.

 

Classics of Recreational Math

The classical recreational math authors are Lewis Carroll,  Henry Dudley,  Martin Gardner, Sam Loyd, and Yakov Perelman.

This an example of classical math puzzles: https://www.aplusclick.org/k/5423.htm :

(10² + 11² + 12²) – (13² + 14²) = ?

The picture “Mental Count” of Russian painter Nikolay Bogdanov-Belsky contains the simple calculation. Image source : Wikipedia

 

Project Starters

Challenging puzzlers to create a positive attitude to real projects.

Project Starters – Curious Questions about Project Management Practice from Igor Kokcharov, Ph.D, PMP