Le meilleur score possible au 2048 : 131072

Math Online Tom Circle

Download 2048 Game:
https://play.google.com/store/apps/details?id=com.estoty.game2048

This addictive game “2048” is better than any other violent game like “The World of Warcraft”. At least it improves your math!

The video explains its principle and why you will never exceed 131,072.

It is binary arithmetic, or power of 2 = $latex 2^{n} &s=3$

image

Notice the rule of 0 & 1:
$latex 32 = 1underbrace {00000}_{5 : zero}$

Minus 2:
$latex 30 = 1111underbrace {0}_{1 : zero}$

Minus 4:
$latex 28 = 111underbrace {00}_{2 : zero}$

image

The maximum scenario whereby all 15 boxes are filled with the power of 2:

Final score (Maximum)
$latex 131,072 = 1underbrace {00,000,000,000,000,000}_{17: zero} = 2^{17} $

Case 1: The 16th box: – 2
$latex 131,070= underbrace {1111111111111111}_{16 : one} underbrace {0}_{1: zero}$

Case 2 (Maximum) : The 16th box: – 4
$latex 131,068 = underbrace {111,111,111,111,111}_{15 : one} underbrace {00}_{2: zero}$

image

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