Explain/solve the Matching Problem in the simplest terms

[redphoton]

Explain/solve the "Matching Problem" in the simplest terms

How would you explain and solve the "Matching Problem" to a HS math club? give the simplest explanation and solution you know.

 

[Dragonfall]

You mean the stable matching problem, from graph theory?

 

[redphoton]

matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."

 

[mXSCNT]

There are many different problems involving matching one set against another.

 

[Dragonfall]

matching problem like the classic: "An absent-minded secretary prepares n letters and envelopes to send to n different people, but then randomly stuffs the letters into the envelopes. A match occurs if a letter is inserted in the proper envelope. Find the probability a match happens."

If P is the probability that a match DOESN'T happen, then 1-P is the probability that a match happens. Is this what you want?