## Motorway Problem

July 12, 2019 Leave a comment

How to choose the shortest road that connects several towns. This is a story about local and global minimums. Excellent presentation of soapy films.

Math and Logic Puzzles

July 12, 2019 Leave a comment

How to choose the shortest road that connects several towns. This is a story about local and global minimums. Excellent presentation of soapy films.

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April 10, 2016 Leave a comment

Dan Finkel suggested principles of extraordinary math teaching:

Math can the best of time or the worst of time.

1) Start with a question.

2) Thinking happens only when you have time to struggle.

3) (Teacher), you are not the answer key.

4) Say yes to your students’ ideas.

5) Play!

A marvelous quotation is attributed to the most brilliant scientist of the modern age, Albert Einstein: “Play is the highest form of research.”

December 13, 2015 2 Comments

**Leslie Green’s Casino Problem**

A bunch of Physicists, fresh from College, go to their local casino with plans to profit with their advanced gaming strategies for Roulette. They have chosen a Roulette game where there are 36 numbers from 1 to 36, alternately colored black and red. There is only one green slot, which is usual in Europe but *unusual* in the USA. When the ball lands in the green slot, 0, all bets are lost to the House.

All participants place 223 bets. Each bet pays out at 1/1 odds, meaning you get your bet back plus an equal amount of winnings.

John bets only on RED, and only immediately after a run of 3 reds.

Sally bets only on EVEN, but only after the sequence ODD, ODD, EVEN, ODD.

Peter looks for a run of 8 events, either all ODD, all EVEN, all RED or all BLACK. He then bets against this run continuing.

At the end of the 223 bets, who is the most likely to have won?

**Leslie Green’s Sports Betting Problem**

The all-male under-10 football team, the Hunky Heroes, are playing the all-girl under-12 football team, the Girly Girls. I am facilitating the betting, *although this may not be strictly legal in all jurisdictions*.

Buddy and his friends have put a total of $200 on the favorites, the Hunky Heroes, to win. If they win I have to pay out a total of $3 for every $2 placed.

Samantha and her friends have put a total of $50 on the Girly Girls to win. If they win I will pay out a total of $6 for each dollar placed. (Some people would call this 5/1 odds, where you win $5 for each dollar placed AND you get your $1 bet back).

Some of the parents have individually placed a total of $100 on a draw. In this case I pay out a total of $3 for each dollar placed.

Who has the greatest chance of winning?

**Casino Statistics**

In a casino on a Sunday, 90% of the visitors lost $200 each, # 9% of the visitors lost $1,000 each, and # the rest won $10,000 each. # If the profit of the casino is $340,000, how many people visited the casino?

**Bankrupt Business**

Jane and Gerry visit a casino. In one game, they have a 1/5 probability of winning $100 and 1/2 probability of losing $50. They have also a chance of no win / no loss. What is the most likely amount of money they will win (or lose) at the end of 100 games?

**Gambling is bad for your health and budget!**

May 1, 2014 Leave a comment

Math can be really practical and useful!

For students.

For lock breakers.

For car racers.

For pool managers.

For family folks.

April 1, 2014 Leave a comment

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.

For 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**

I 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?

February 12, 2014 Leave a comment

Dan Hurley:

You get better as you practice.

Working memory exercise 20 minutes a day 5 days per week

gives perfect results.

February 1, 2014 Leave a comment

Math is fun. Ten sample problems prove that math and logic can be interesting. It provides a link to collection of challenging math and logic puzzles.

Can be Math Funny? Try to solve 10 problems from A+Click.