first of all you sound a bit haughty and arrogant, we are all friends here. no need to be rude

secondly, who said anything about "give for free the hard-earned money"? equal distribution does not mean expropriate and redistribute. it means redestribute on market base principals. reflow from the oceans to the local seas, ponds, puddles and cups. how to do it? i don't know. is it possible? i don't know. will it make the world a better place? i don't know. will it kill bitcoin or immortalize forever? i don't know.
the point is that people's money has to be people's money/
You are not the first coming with this ideas and it's rather frustrating to see them pop up over and over again.
Or maybe you didn't know how to express yourself and convince me. If it "does not mean expropriate and redistribute", then how could you (or the entity redistributing) acquire all those coins, from which some are private property and some are not even mined (and the miners will obviously won't mine them for free)?
how to do it? i don't know. is it possible? i don't know. will it make the world a better place? i don't know. will it kill bitcoin or immortalize forever? i don't know.
This is the part I like. It's the part you no longer sound like you want to teach us how to do it, instead you become open for discussion.
I'll answer, from my point of view:
* how to do it: for Bitcoin you cannot. Only somebody willing to give his own Bitcoin would be able to do that and it'll be with a small fraction of all Bitcoin. That's why I said in a later post to make a new coin for it. You'll have to premine it and send it.
One problem is that nobody will waste electricity for free to send your transactions, since you don't plan to pay them and you may not even have coins for paying them.
Another problem is that if you give it to everybody, it doesn't make it valuable. What's the difference from giving everybody air, water or some sand? Not much...
* is it possible: with a new coin or token, if you also pay the miners (or do some centralized approach) it is possible, but completely useless, because it will bear no value and people will not care about it (and probably won't redeem it)
* will it kill bitcoin or immortalize forever: if it would be possible for Bitcoin it will probably ruin its price.
* will it make the world a better place: nope, sorry. People will either waste the free money, either not hear/care about it or have no means to access it. And if I'm wrong and people will access it, the more access it, the lower its price will go, since most will sell asap for more palpable fiat or food, (or drink), and in a year it will be an old fun story, nothing more.
As you see, I try to give scenarios, not related between each other because the exact thing you "proposed" cannot be done.
Clearer now?
PS. Also the representation of your math is wrong. If you divide Bitcoin to people you obtain Bitcoin. So you'll have to either write Bitcoin as measure unit, either multiply with 10^8 to obtain satoshis.