5 ms·

I don't see how that line of thought helps you solve this problem. Can you elaborate?

• patio11 15y ago
  It's the start of a very, very informal argument that the optimum number of randomly assigned objects for any N containers to maximize the number of individually packed containers is N. This problem asks you for what happens if N = 365.
  • jules 15y ago
    It's just that I don't see the pattern: a) A special act of Congress has made the year only one day long. How many employees would you hire? It doesn't matter, because the people you hire will have their birthday on this day. b) Congress extends the year by one day. Think quick: hire, fire, or no action? Hiring one person gives you 1 workday. Hiring two people gives you 2 workdays with probability 1/2 and 0 workdays with probability 1/2, so the expected value is 1 workday. Hiring 3 people gives you 3 workdays with probability 1/4 and 0 workdays with probability 3/4. So that gives you expected 3/4 workdays. c) Congress extends the year by one day. Think quick: hire, fire, or no action? 1 person: 2 workdays 2 people: 1/3*4 + 2/3*2 = 8/3 3 people: 1/9*6 + 6/9*3 = 8/3 4 people: 1/27*... = ... d) Congress extends the year by one day. Think quick: hire, fire, or no action? That is getting complicated. Obviously I'm missing something here. Can you reveal the insight?