Strong Induction

We need medicine to protect from biological warfare.

This is Strong Induction, and P is prime numbers.

You need to destroy orange boxes which are n(n+1)/2. White boxes are n(n-1)/2.

[n(n+1)/2]+[n(n-1)/2]=n^2

You have 5 boxes, and you divide them. Finally they become one box. You get the score, 6+3+1=10. This is n(n-1)/2.

At first, you have n boxes. Then, you get points when you have n-1 boxes. The final points are (n−1)+(n−2)+· · ·+2+1.

∴

You prove P(n+1). You have k boxes. k(n+1-k) is the first step to get a point. Every strategy for n boxes leads to a score of n(n − 1)/2.

∴

α=(i)+(ii)+(iii)

You are saved. [n(n-1)/2]^2 is also the square. P(1)=0. Viruses are still somewhere. P(k)≧2. You need to divide it, and it is prime numbers.