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.

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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

 

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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.

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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?

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Leslie Green gives the answer : 96 days.

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

 

 

Mensa Tough Puzzle

Tough question from A+Click makes you crazy. 99.9% fail or refuse to solve it.aplusclickQuestion

Funny Questions and Unexpected Answers at Tech Job Interview

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Mr Barton’s Web Whizz Video on A+ Click Math

“I love NRICH, & whilst it remains my number one stop for rich maths puzzles & problems, this website might just be number two. There are literally 100s of puzzle & problems for students to solve. They are beautifully laid out on the page, making them absolutely ideal to project on the board to use as starter activities or extension work. I also suggest using them in the computer room as the website keeps a handy record of students’ progress through a series of puzzles. With the development of students creative thinking & problem solving growing in importance, this website is a must!” – Craig Barton

A+Click SMS Part 4

SMS stands for Short Math Situation. The SMS questions are limited to 64 characters.

91. How many 5-digit passwords are the same backwards as forwards? Answer

92. Which digit do I use less if I number 999 pages? Answer

93. How many digits are there in the result of 1001 power 11? Answer

94. How many are there symmetrical capital letters of the alphabet?  Answer

95. Four cowboys fired once. What is probability that all are dead? Answer

96. What is the largest sum of two integers which product is 787? Answer

97. The time left today is half of the time passed. What’s time now? Answer

98. How many trials are needed to identify 3 keys for 3 keyholes? Answer

99. How many 2-digit integers have the sum of the digits equals 10? Answer

100. How much paper is needed to entirely cover a 40x30x12 box? Answer

101. How many apples were sold if 33, or 11% of the total, are left. Answer

102. What area does a line cover? It is 0.25 mm thick and 8 km long. Answer

103. 3 apples weigh in pairs 200, 204, and 208. Find their weights. Answer

104. What is the angle between the hour and minute hands at 14:20? Answer

105. How many small pieces of cheese you can get using only 5 cuts? Answer

106. How many Ancient Olympic Games were held from 776 BC to 393 AD? Answer

107. How much ribbon do you need to wrap around a 12x30x40 box? Answer

108. How many 7-digit phone numbers are there?  Answer

109. Estimate the height of a lighthouse from which I can see 11km. Answer

110. Which days of the week occurred more frequently in 2012? Answer

111. 33 years, 33 months, 33 weeks, 33 days,  33 hours. How old am I? Answer

112. What is the smallest 5 digit integer with 5 different digits? Answer

The full collection of 100 SMS can be found at A+Click SMS.