## Complex Problem Solving is Your Top Skill

Be ready for the Fourth Industrial Revolution!

According to the new World Economic Forum Report “The Future of Jobs” the most required skill is Complex Problem Solving together with Creativity and Critical Thinking.

Train yourself! Start with simple problems, for example, at Aplisclick, do it regularly and grow your most important skill.

Daan Roosegaarde uses technology and creative thinking to produce imaginative, earth-friendly designs and highlights the importance of the problem solving skills.

“There are no passengers on spaceship earth. We are all crew.” – Marshall McLuhan

## 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?

## Consumer Math

#### Leslie Green’s Question

The more debt you get into, the more credit card companies profit. If you buy \$100 of goods at a shop you owe the credit card company \$100, but typically the shop only gets \$98. The shop has to inflate its prices to pay the credit card company. Typically the shop is contractually not allowed to give a discount for cash.  The CostCrashers supermarket chain deals only in cash. The CardPayers supermarkets deal with both cash and credit card transactions, although 75% of people pay by credit card.  All else being equal, how much cheaper could the CostCrashers prices be compared to the CardPayers supermarkets, given the figures stated earlier?

My car uses 10 litres / 100 km and has a 70-litre tank. The Village Garage sells fuel for \$1.40 per litre. It is just several meters from my house. Several garages outside the village sell fuel for \$1.36 per litre. How far could the garage be so that it is worthwhile to drive to and back from the garage to refuel?

#### Income

Bob works 40 years. He does not work on weekends and has a 3-week summer vacation and 7 days of official holidays. The average hourly rate is \$12.5 and he works 8 hours per day.  What is his total income?

#### Stock Price

Every day, a stock price of \$444 is either increased or decreased by 4%. When can it be \$444 again?

#### Inflation

If there is a 500% inflation in a country how much will a 2-dollar telephone cost in one year?

#### Discount

Two successive increases of 25% and 25% are followed by two successive discounts of 25% and 25%.  What percentage is the result?

#### Selling Luxury Cars

If 2 salesmen can sell three luxury cars in 4 days, how many luxury cars can five salesmen sell to six clients in 7 days?

#### Ratio 1 : 2 : 3

Divide \$132 into a ratio 1:2:3. What are the parts?

#### Rebate

Buy 2 for the price of 3 and get 50% off! What is the final rebate do you get?

You find the answers to these and hundreds other Consumer Math’s challenges at http://www.aplusclick.com/money.htm

## 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. http://www.meritcd.com

## Geek’s Questions: The Art of Asking Yourself

A+Click contributor Gerry Geek just published a new true story:

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?

## Math Magic: To Predict Unknown

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?

## Think Outside The Box

Thinking Outside The Box or Thinking differently is the first step of innovation.

The slides show 10 examples of such problems.

100 outside-the-box questions are presented at www.aplusclick.org/ThinkOutsideTheBox.htm

## Brain Teaser Interview Questions and Answers

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?

## AN INTERVIEW QUESTION AT GOOGLE

I confess that I was not on top during an interview for a job at Google. The interviewer was the manager who gave his name to one of the social networks. He was very nice guy. He asked me a question:

“What is your strategy to find your car along a very long street if you don’t remember the parking place?”

Being under interview pressure, I quickly improvised an answer like this: I double the distance every time I change direction.

The mathematically correct answer might be the linear search.

To go X blocks (cars) in one direction, then 2X in the other, then 4X forwards, 8X in the reverse direction etc… The initial X depends on the standard deviation.

Now I have time to think about the real problem, I find that the theoretically correct answer is not correct for real life. My mistake was sticking to the initial data; I did not think about the real situation. There are no infinite streets in real life.

One of the practical approaches is : choose a direction and go until the end;  if I am not lucky, then go in the other direction.

When I ask a manager about the solution he said: “I will use the key signalization to find my car.” This is “a management solution”.

Is this problem an example of the math paradox: the theoretical solution is not the same as the practical choice? There are many anecdotes about mathematicians: mathematicians are absolutely right and absolutely useless.

Here the list of 140 questions at Google: