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arglebargle
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A crazed billionaire has a lifelong dream to build the world's tallest structure as a testament to his glory. Fearing competition, he decides that his tower must be far taller than any other in order to remain that way for as long as possible. The goal: build a 10 km tower, and do it in as little time as possible.
At his disposal are 1 m high x 100 m wide square blocks and special cranes/lifters. These lifters are capable of lifting as many as 5000 stacked blocks at a time and placing them on top of another stack. However, there are some limitations.
Placing a block on top of another block takes 1 week.
Similarly, placing a stack on top of another stack also takes 1 week.
However, if either of those stacks is taller than 100 m, this process takes 2 weeks.
Naturally, stacking a group of blocks or stacks precludes the possibility of doing anything else to that group during the same week (one operation per block or stack per week).
Our billionaire will spare no expense in the construction of this tower. Thus, the number of lifters and blocks is unlimited.
Using these unlimited resources, what is the smallest number of weeks in which the tower can be completed?
What method should be used to achieve this goal?
At his disposal are 1 m high x 100 m wide square blocks and special cranes/lifters. These lifters are capable of lifting as many as 5000 stacked blocks at a time and placing them on top of another stack. However, there are some limitations.
Placing a block on top of another block takes 1 week.
Similarly, placing a stack on top of another stack also takes 1 week.
However, if either of those stacks is taller than 100 m, this process takes 2 weeks.
Naturally, stacking a group of blocks or stacks precludes the possibility of doing anything else to that group during the same week (one operation per block or stack per week).
Our billionaire will spare no expense in the construction of this tower. Thus, the number of lifters and blocks is unlimited.
Using these unlimited resources, what is the smallest number of weeks in which the tower can be completed?
20 weeks
What method should be used to achieve this goal?