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 = $latex 2^{n} &s=3$
Notice the rule of 0 & 1:
$latex 32 = 1underbrace {00000}_{5 : zero}$
Minus 2:
$latex 30 = 1111underbrace {0}_{1 : zero}$
Minus 4:
$latex 28 = 111underbrace {00}_{2 : zero}$
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
$latex 131,068 = underbrace {111,111,111,111,111}_{15 : one} underbrace {00}_{2: zero}$
Mathtuition88 