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?

married

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”

married

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: Image

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.”

Really Practical Math

Math can be really practical and useful!Image

For students.

ImageImageImageImage

For lock breakers.

For car racers.

For pool managers.

For family folks.

 

Math Magic: To Predict Unknown

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One of the math magic is to predict unknown facts. Please find below several situations where math gives unexpected and useful answers.

1. Code Testers

John detected 2 errors and Mary – 3 errors in a code. There is one error in common. How many errors are still undetected?

It looks like a joke. However there is a mathematical solution of the problem that shows that the number of undetected errors is N. I am sure that you can easily to find the number N.

99.9% fail or refuse to solve it.

 

2. Lake Width

 

How estimate the width of a lake without crossing it? You just walk and make some measures at a lakeside.

 

ImageFor example in the situation shown at the picture the width of the lake is 200 meters.

 

3. How many fish are there in the lake?

Yesterday, I caught 30 fish of a certain size in the lake.
I marked and released them without any harm.
Today I also caught and released 80 fish of the same size and noticed that there were 6 marked fish in the second catch.

How many fish of the same size are there in the lake?

4.  Seller’s decision

ImageI sell my car. People come to my garage one at a time and make bids to buy it. I make an immediate decision whether to accept or reject an offer after receiving it. I decide to reject the first N offers, mark the highest price P, and accept the first offer that is greater than P.

What number N do you recommend me if I expect that 100 people can make a bid?

If N is small, I can accept a small amount of money.
If N is large, I can reject the best offer.

This is the famous problem of the optimal stopping theory (Secretary Problem).

5. Winning Strategy

In a game, Anna and Bill take 1, 2, or 3 coins on each turn. The player to take the last coin from the pile wins. If Anna goes first and there are 40 coins on the table, how many coins should she take to guarantee that she would win?

The truth is “She always loses if Bill knows the winning strategy.” Do you know Bill’s strategy?