House of Cards

Suppose you're building a house of cards in your garage. At the beginning, you have a messy pile of cards lying on the ground. It takes you a long time to get the basic structure going (a three level house of cards). Once you have the basic structure, you can finish the house very quickly (gluing the cards together, to fix the structure permanently). However, the glue is very toxic, so you have to fix the structure outside. During this time, the assembled house of cards is susceptible to an intermittent wind, that can knock it down entirely.

How long on average does it take you to finish the house of cards (in hours)?

Assumptions and Details

  • It takes exactly 10 minutes to build the basic structure.
  • Once the house of cards is built, it takes sixty seconds to reinforce with glue.
  • Once the house of cards is standing, a wind comes by at random an average of once every twenty seconds (\(k_\text{wind} = \frac{1}{20}\) s\(^{-1}\)).
  • If the wind comes before the house is completely reinforced, the house will collapse.

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