Car Owner’s Puzzles

Can a specific subject provokes interest to Math?

For example, cars. How much does the gas cost in a month? What speed to choose? When do I need to change the tires? How to be on time? How much do I pay for a car during its life? . . .

 

What are other intersting subjects? Finance? Love? Sport?

Work Hard – Aim High

Wikipedia article on Skills

Teacher’s job is not teaching

Teacher’s job is not teaching. Teacher’s job is helping students to learn.

Students learn ( Math )  to be able creating value for others in the future.

WSJ: Mathematician is The Best Job

Starting from 2009, The Wall Street Journal repeats “Another day, another reason to get better at math.” Mathematicians top the list of the Best Job:

The 10 Best Jobs of 2014Financial charts with lighthouse on the background

There are not many positions that are called “mathematician”. When you are good in math you work as a Problem Solver and have different titles: engineer, project manager, CIO, CTO, CEO, software engineer, business developer, etc.

Choose the Best Job = be good in Math!

How to Make Decisions: Slow or Fast?

The mind makes 35,000 decisions a day.

Half of all business decisions end in failure.

Data-centered decision-making results in 5-6% productivity increase.

Make your decision based on data and reasoning (when it is possible).

(c) 2014 Merit Career Development.

(c) 2014 Merit Career Development. http://www.meritcd.com

Math Magic: To Predict Unknown

Image

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?

 

 

Brain Teaser Interview Questions and Answers

Image

Brain Teaser Interview Questions and Answers

answers brain teaser interview questions that are commonly asked at job interviews for technical and quantitative roles. These questions focus on problem solving, spatial reasoning, and understanding.

By reading this document, you’ll be better prepared to answer unexpected questions, think outside the box, and elaborate on non-standard solutions. And most importantly, you’ll be calm and relaxed at the interview.

Answers to  brain teaser interview questions including:

    • How do you find your car along a very long street when you don’t remember where you parked it?
    • We want to merge 4 companies into one large company. How many ways are there to merge them?
    • I have a rectangular piece of cheese with a round hole. How do I cut the piece with one straight lien into two parts of equal weight?
    • There are a number of stones, all of different weights. The 10 lightest stones weigh 40% of the total weight. The 5 heaviest stones weigh 25% of the total weight. How many stones are there?
    • What is the avg. of the smaller of three random numbers of 0 to 1?
    • “1” costs $10. “20” costs $20. How much does “100” cost?
    • It takes 6 people 48 hours to paint a house. How long would it take to paint the house if 3 people were added to the middle of the project?
    • 3 apples were weighed in pairs and the weights were 200, 204, 208 grams. What is the weight of the lightest apple?
    • You are shrunk so that your height is equal to the diameter of a dime (a ten-cent coin) and your mass is proportional reduced so as to maintain your original density. Who is heavier, you or the dime?
    • I roll two dice. What is the probability that the 2nd number is greater than the 1st?