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How to Find a Spouse A Problem in Discrete Mathematics With an Assist From Calculus. The Rules of the Game. It is generally considered bad form to date seriously two different people simultaneously , so you consider each person one at a time. You can date someone for any - PowerPoint PPT Presentation
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How to Find a SpouseA Problem in Discrete Mathematics
With an Assist From Calculus
The Rules of the Game
• It is generally considered bad form to date seriously two different people simultaneously, so you consider each person one at a time.
• You can date someone for any length of time, but eventually, you must either “select” them or say “no”and move on to another candidate.
• Once someone has been passed over, you cannot go back. No is forever.
If there are N candidates, how can you maximize the probability that you select your best match?
Alternative Interpretations• Choosing largest number in a pile
• Hitting a slow-pitch softball
What’s a good strategy?
The “Take the First Pitch”
Strategy
Fix N
A Mathematical Model
1
prob of being in Position prob of being selected given they are in PositionN
n
P k n n
Our Probability Function
Can Calculus Help?
Calculator Program
But, Calculus Can Help
1 1 1 1
1 2 1
N
k
dx
k k k N x
Differentiable Approximation1 1 1 1
1 2 1
N
k
dx
k k k N x
Define a Continuous Variable
What is Our Probability of Success?
The Moral?