Download How to Find a Spouse

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
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
N
P  k     prob of being in Position n  prob of being selected given they are in Position n 
n 1
Our Probability Function
Can Calculus Help?
Calculator Program
But, Calculus Can Help
1
1
1



k k 1 k  2
N
1
dx


N 1 k x
Differentiable Approximation
1
1
1



k k 1 k  2
N
1
dx


N 1 k x
Define a Continuous Variable
What is Our Probability of
Success?
The Moral?