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

AplusclickThinkOutsideTheBox

You Are A Math Genius!

Everybody was born a genius! You too!Young and Successful

Unleash the genius that sleeps within.

How? Make your brain work!

One of the possibilities is a small everyday dose of brain work.

Look at the puzzle below.

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At the beginning, it can drive you crazy.

Don’t give up!

Take an easier challenge and GROW!

Aplusclick provides you with an enormous opportunity for everyday training!

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You start with unpractical number puzzles and finish by solving practical optimization problems such as finding the shortest underground route …

… or packing the maximum possible number of boxes in a room.

Remember: You are a genius! Don’t miss an opportunity to grow!

A rendezvous at www.aplusclick.orgImage

Beautiful Math Problems

What are characteristics of the most beautiful math problems?

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They are practical, they give an impression that the problem cannot be solved, and finish by an unexpected (surprise) solution.

It is not about the beautiful math equations or mathematical beauty. It is mostly about recreational math, brain teasers, and thinking outside the box.

Find a short list of my favourite beautiful problems:

1. Morozkin’s problem:

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Vladimir Arnold (1937-2010), one of the greatest 20th century Russian mathematicians told the following story:

“Our schoolteacher I. V. Morozkin gave us the following problem: Two old women started at sunrise and each walked at a constant (different) velocity. One went from A to B and the other from B to A. They met at noon and, continuing with no stop, arrived respectively at B at 4 p.m. and at A at 9 p.m.  At what time was the sunrise on this day?”

Solution

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2. Martin Gardner’s favorite problem

“Three sailors come across a pile of coconuts. The first sailor takes half of them plus half a coconut. The second sailor takes half of what is left, plus half a coconut. The third sailor also takes half of what remains, plus half a coconut. Left over is exactly one coconut, which they toss to a monkey. How many coconuts were in the original pile?”

Solution

3. Lucas problem

François Édouard Anatole Lucas (1842 – 1891) was a French mathematician.

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Every day at noon, a ship leave Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many ships will a ship leaving Le Havre today meet at sea?

Solution

4. Euler bridge problem

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In a city Konigsberg, there were seven bridges. There was a tradition to walk and cross over each of the seven bridges only once. If a person starts and finishes at the same point, can he accomplish this task?

Solution

5. Secretary problem

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An entrepreneur wants to hire the best person for a position. He makes a decision immediately after the interview. Once rejected, an applicant cannot be recalled. He interviews N randomly chosen people out of 100 applicants, rejects them and records the best score S. After that, he continues to interview others and stops when the person has a score better than S. What number N do you recommend to the cruel man?

Solution

6. Monty Hall

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A venture capitalist will invest in only one of three start-up companies: A, B, or C. I will make a lot of money if I invest in the same company, and will lose all of my money if I choose another company. I decide to invest in company A and I inform the venture capitalist. He assures me that he does not invest in company C. What company do you recommend for me to make the investment?

Solution

7. The Legend of Carthage

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The Legend of Carthage: Queen Dido and her followers arrived in North Africa. The locals told them that they could have the coastal area that an ox hide would cover. She cut the hide into a series of thin strips, jointed them together, and formed a coastal shape. The ox-hide enclosed area was known as Carthage. If you had a 10 km long strip, which shape (rectangle, triangle, semi-circle, or semi-ellipse) would you choose to maximize the enclosed area?

Solution

8. Lewis Carroll’s Coaches

twotrainsA coach leaves London for York and another at the same moment leaves York for London. They go at uniform rates, one faster than the other. After meeting and passing, one requires sixteen hours and the other nine hours to complete the journey. What total time does each coach require for the whole journey?

Solution

You are welcome to expand the list by submitting your input at the website www.aplusclick.org

 

Why choose Math at A+Click?

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Practice is the best way to develop math skills, special thinking, and logical reasoning.

More than 271 million pages are returned for the keyword search “puzzle” on Google. Furthermore, tons of pages, books, and games include puzzles, questions, and problems. Which one do you choose?

Many students choose A+Click. Why? What distinguishes A+Click from other web pages? Below is the answer:

1) It has interesting, diverse questions

2) Everything is simple and visible

3) It has international competitions, statistics, and certificates

4) Everybody can have a go, even adults

5) It works on all computers, tablets, iPads, iPods, and smartphones

6) It offers endless problems (3600+ questions)

7) No charge

8) No advertising

9 ) No sign in

Certainly, we can easily find sites or books with some of these features. A+Click distinguishes itself from others by collecting all of them together. It unites the expertise of dozens of experts such as math teachers, puzzlers, logicians, and curious people in one of the simplest forms available.

“I am always ready to learn although I do not always like being taught.” – W.Churchill.   A+Click does not teach, it gives an opportunity to learn.

Learning is doing, not watching. Learning is active, not passive.

The A+Click team hopes you will find the collection interesting and useful. Try it at https://www.aplusclick.org

Brain Teaser Interview Questions and Answers

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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

ImageI 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:

http://www.impactinterview.com/2009/10/140-google-interview-questions/

Recently, the senior vice president of people operations at Google admits that certain brainteasers are useless.

When I applied to my recent job, there were not formal interviews. We just discussed business development. At a dinner, the company owner asked funny coin puzzles. I was the first who correctly answered. I got the job.

I still think that such challenges are very useful. I do it.  Engineering and non-HR managers still informally use such questions.

I did not get the job at Google and I am happy about that. Since that time, I have collected logic problems and put 150+ questions/answers into a book titled Job Interview Logic Puzzles. This is a great help for engineers and managers who want to be ready for challenging interview questions.

Math: Practical Problems for Human Beings

 

There are many books Practical Problems in Math for Electricians, for Health Careers, Welders, etc. Nice!

Why there are not math Q&A just for people?

We tried to compile some of them in the presentation.

Enjoy!

 

Funny Questions and Unexpected Answers at Tech Job Interview

Brain Teaser Interview Questions And Answers on Amazon

Brain Teaser Interview Questions And Answers on iTunes

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

The Best Math Word Problems

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What are real-life math problems?

What are the funniest word problems?

What are the shortest word problems?

What are the most difficult word problems?

What are the best word problems?

Math and logic word problems. Here my preferred word problems go:

Practical:

How many tennis balls can fit in a school bus?

A goldfish need 1000 cubic inches of water to live in. 
An aquarium is 20 inches in diameter. 

How many fish can live in an aquarium?

Funny:

1 costs $10; 20 costs $20. How much does 100 cost?

99% of nuts and 99% of a nut cost as much as all nuts. How many nuts are there?

At least two Londoners have the same number of hair. Correct?

80% of IT projects fail, and 20% of managers are female. How many male managers succeed?

Short:

Does clock hands overlap 22 times in 24h?

How many zeros are at the end of 99!?

Make 33 by using three 3s and any signs.

Difficult:

Six Millennium Prize Problems set by the Clay Mathematics Institute have yet to be solved.

http://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics

The Best:

Short + Funny + Practical + Difficult = Best

My preferred math and logic word problems are at www.aplusclick.org

The latest collection of the best free A+Click Puzzles are at Apple App Store

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