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Can you guess the next letter in this series? and why?

C Y G T N L I T ….?

You see the following special offer by the convenience store:

” A bottle of Choco Cola for every 3 empty bottles returned “

Now you decide to buy some (say N) bottles of cola from the store. You would like to know how you can get the most cola from them.

The figure below shows the case where N = 8. Method 1 is the standard way: after finishing your 8 bottles of cola, you have 8 empty bottles. Take 6 of them and you get 2 new bottles of cola. Now after drinking them you have 4 empty bottles, so you take 3 of them to get yet another new cola. Finally, you have only 2 bottles in hand, so you cannot get new cola any more. Hence, you have enjoyed 8 + 2 + 1 = 11 bottles of cola.

You can actually do better! In Method 2, you first borrow an empty bottle from your friend (?! Or the storekeeper??), then you can enjoy 8 + 3 + 1 = 12 bottles of cola! Of course, you will have to return your remaining empty bottle back to your friend.

what is the maximum number of bottles of cola you can enjoy if you started with 153 bottle?

Note: Drinking too much cola is bad for your health, so… don’t try this at home!!

Back to the Challenge

The map below shows the street locations of a city. Position the minimum number of police officers so that any point on any street can be seen by at least one officer.