Some people stay home when it snows. Let us say that with 5 cm of snow, 10% of people stay home. With another 5 cm, 10% of the 90% also stay home. Another 5 cm, and 10% of those who braved the outdoors at 10 cm also stay home. And on and on at each 5 cm, 10% of those who braved the weather at the previous snow level decide that home is where the hearth is and ask the others where the hot chocolate is anyway.

How much snow does it take to have at least half of the general population stay home?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, January 28, 2015 at noon Pacific Time.** I will post the answer shortly after.