Pinochle Numbers (UMAP)

Author: Richard Iltis and Tom Linton

This module uses the setting of the card game of pinochle to develop and practice counting techniques, including combinations, generating functions, Polya's block walking, inclusion-exclusion, and fixing types.

Table of Contents:

INTRODUCTION

COUNTING DISTINCT HANDS
Combinations
Generating Functions
Inclusion-Exclusion
How Many Hands?
Special Hands
The Pinochle Triangle
Block Walking
Three Summation Identities
Pinochle-Number Identities

COUNTING FOR PROBABILITIES
Probability of a Pinochle
Via combinations
Via permutations
Via the complement
Via generating functions
Fixing Types
The Original Exam Questions
More about the Game of Pinochle
More-Challenging Problems
Basic method
A pinochle plus an around
A pinochle plus a marriage
A pinochle plus an around plus a marriage
Further computations

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHORS