Real Mathematics – Puzzle #3

Story of Magic Baklava

Some of you may have heard the story of Excalibur which was about the magical sword of King Arthur of Britain. It was a special sword indeed because the person who was in possession of Excalibur would gain superhuman powers. This is why Excalibur could be counted as a mythological story.

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In this article I will be talking about another mythological story. A story which I found in a very old book… A story that might sound unfamiliar to you: Serkan’s magic baklava.

Unlucky Dad

This is a true story that was lived 2700 years ago in the soils of modern Turkey.

Serkan’s father was born in Mardin, an ancient city that is located in the heart of Mesopotamia where first known civilizations flourished. He was the most popular baklava chef of his time until a traumatic event occurred. When Serkan was born, his father made free baklava to celebrate the birth of his first child. Unfortunately eight people were poisoned and hospitalized because of bad baklava…

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A baklava master in the modern day.

Serkan’s father could not overcome this horrific event: Eventually he swore that he will never touch another baklava.

Birth of Magic Baklava

Years passed. Serkan was working with a shoe master to help his family financially as he was also an average senior in high school. University entrance exam was just one week away and Serkan’s guidance teacher was handing out candy to everyone in his class. (In modern Turkey it is a tradition to have candy with you in exams as elders believe that it helps you to get a better grade.)

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Oh orange candy…

There were two kinds of candies: Orange and mint. Serkan wanted orange but was left with mint candies. When his father saw Serkan with a sad face, he thought that it was time for him to help his beloved son. Next morning he woke his son:

“Son! I broke my vow once and for all and made a magic baklava for you. After eating this magic baklava, you will have superhuman powers and every question shall bow before your pencil! Harvard or Oxford, all the universities in the world will be yours thanks to this magic baklava.

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Magic baklava

Although, you have to prove that you are worthy of this baklava. This is why I prepared a riddle for you.

  • Baklava is inside one of the four boxes.
    madobak
  • Until the exam morning, you can select one box a day.
  • Every day I’ll be changing the box of the baklava.
  • I’ll be putting the baklava only to its neighbor box. Eg. if baklava is inside box number 1, I should move it to its only neighbor box number 2. If it is inside box number 2, then I should move it to either one of its neighbors box number 1 or 3.
    maddo
  • Find the baklava before your exam.”

This story is known as the most realistic story of mythology. Even after 2700 years, it is still being told.

Questions

  1. How can Serkan find his magic baklava?
  2. Is there a sure algorithm for that?
  3. What if there were 5 boxes? Or n boxes?

M. Serkan Kalaycıoğlu

Real Mathematics: Game #3

Chocolate Box

A dear friend of mine started a new business recently. I bought a box of chocolate with the intention of visiting his store. Eventually I did visit his store. Although I could not stop myself opening the box before my visit. In the end I murdered almost half of the box. Sorry matey!

Today I checked what is left in the box and I realized something: Why aren’t same types of chocolates in the adjacent compartments?

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Being Neighbors

In order to avoid neighborhood between same types of chocolates, we should be careful not to place them as shown in the photo.

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Let’s call this rule “sufficient chocolate density”, or “S.C.D.”.

Question 1: Assume that you have four different types of chocolates and seven chocolates from each type. Could you have S.C.D. in such a box like the following photo?

Question 2: What is the least number of different chocolate types you can place inside this box?

Question 3: In case you have a box like shown below, at least how many different types of chocolate do you need to maintain S.C.D.?

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Question 4: If you had four different chocolate types and nine from each type, could you be able to construct a box that has S.C.D.? If yes, what would it look like?

M. Serkan Kalaycıoğlu