The Printing of Money for Paying Debt
Printing money causes inflation because someone (or some institution) will get the money and will spend it somehow. This increases demand for goods, but the number of goods, the supply was not affected by printing money. Hence demand at the old price level is larger than supply at the old price level. Prices will rise until a new equilibrium is reached.

The problem is that you seem to think that the N dollars you give to China would be gone. But it wouldn't be, the people who got it in China can now spend it in the US. They can import things, come as tourists, make investment purchases etc. This increases demand and results in inflation again.