Pancake Math

panecake2“Archaeological evidence suggests that pancakes are probably the earliest and most widespread cereal food eaten in prehistoric societies.” – Wikipedia

 

What is the maximum number of sections into which a pancake may be divided into by four straight cuts through it?

Here more difficult questions go:

1) Is it possible to divided it so that all sections have equal area?

2) How many pancakes are needed to reach your height if they are squeezed by the weight of the upper pancakes?

3) If I spent 30 grams of batter for a pancake (French-style crêpe) of 30 cm in diameter how much batter do I need for the square pancake of the same thickness and the side length of 30 cm?  

 

These and many other practical “pancake” questions are presented in the Applied Math section of A+Click series, which already includes more than 4500 questions.

 

Mensa Tough Puzzle

Tough question from A+Click makes you crazy. 99.9% fail or refuse to solve it.aplusclickQuestion

Really Practical Math

Math can be really practical and useful!Image

For students.

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For lock breakers.

For car racers.

For pool managers.

For family folks.

 

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