**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?

**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.

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.?

**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

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Maths teacher, sports lover and a professional music listener.
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