Towers grow at points along a line. All towers start with height 0 and grow at the rate of one meter per second. When two adjacent towers are *each* at least 1 meter tall, a new tower begins to grow at a point along the line half way between those two adjacent towers. Before time 0 there are no towers, but at time 0 the first two towers begin to grow at two points along the line. At time 1 second, a new tower appears following the rules above. a) How many towers will there be at time 10 seconds? b) What is the sum of all the heights at time 10 seconds?
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