vpalan2

If I wanted to do massive, irreparable harm to China, this is the law I would pass. And yet, they have done this willingly to themselves, without hesitation or incident.

I lost several playlists with a recent ITunes update. Newer upgrades of iTunes have not helped.

Given how basic the concept of a playlist is to iTunes, I was surprised to find this was not fixed immediately.

Here's how I would think about it:

If a number N is composite, then it is a product of two numbers smaller than N. Let's call them n1 and n2.

If both n1 and n2 are greater than sqrt(N), then their product would exceed N, violating the assumption above that they equal N:

N= sqrt(N) x sqrt(N) < n1 x n2

A similar argument applies if both n1 and n2 are smaller than sqrt(N): n1 x n2 is less than N, violating the assumption.

So the only other possibilities are:

a) n1 and n2 are exactly equal to sqrt(N)

b) one of the factors is less than sqrt(N) and the other is greater than sqrt(N)

So if either n1 or n2 are not exactly equal to sqrt(N), then a composite number N must have at least one factor less than sqrt(N).

I wonder how these habits changed towards the end as they were dying out, just before or after the great asteroid that hit the planet.

This is great. As a next step, perhaps make the sliders more mobile friendly?