# Le meilleur score possible au 2048 : 131072

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 = $2^{n}$

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

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

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

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

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

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

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