Tuesday puzzle
Alex Y
Legend has it that in the far north, there was a mighty lumberjack and a small spruce tree. Ten years ago, when the lumberjack was a mere 4' tall and the tree was 8' tall, the lumberjack drove a stake into the trunk of the tree at 1/2 of his height (1/4 of the tree height). He then declared that when the tree had grown to the point where that marker was at his height, he would cut down the tree.
Since that time, the lumberjack has grown at a rate of 1 foot per year (he is a legendary lumberjack, after all). For the next ten years, he will grow at the rate of 11" per year, and his growth rate will continue to decrease each decade by 1", until he finally stops growing. (He won't start shrinking.)
Meanwhile, the tree has grown and will continue to grow at a constant rate of 1" per year.
How long will it be before this legendary lumberjack cuts down that tree?