Printing money to redistribute wealth A fictional country has 100 people. The total printed money is $2000. Ten rich people own half of it ($100 each), the remaining 90 are comparatively poor : ($\$2000 = 10  \times \$100 + 90 \times \$11.11 $)

To make things more even, the government decides to print another $2000 (no independent Central Bank here) and give them to all inhabitants, $20 each. Surely, this triggers inflation, prices double. But the net result is a redistribution of wealth, the poor are now less poor than before. 

This looks as a simple progressive tax scheme which is beneficial to the poorest people. It could even be applied in some periodical and predictable way.

Of course, this is utterly stupid and cannot work - I guess. Why?
The main problem is that wealth does not equal cash. Those ten rich people probably have most of their wealth in real estate and stocks. Imagine all you own is a Lamborghini, then the government prints a lot of money, does that impact you?

Depending on the situation the money printing may be progressive or regressive. And the cost are high: There will not just be one inflationary moment, there will be inflation because the initial inflation breeds an expectation of even more inflation leading to hyperinflation.

Finally when you've done this once, nobody will ever want to hold your currency again because they distrust you. Leading to a number of other problems.