The MathZorro Podcast • Christopher R. H. Hanusa

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A podcast about research in combinatorics by Christopher R. H. Hanusa.

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Episode 1: Card Collecting (mp3, 10min)

Ray Chin discusses his childhood hobby involving card collecting. (Cards such as Pokemon, Yu-Gi-Oh, Magic the Gathering, Baseball cards, etc.) He asks the question "In how many ways can you collect a full set of 10 cards when every deck you buy contains five random cards each." This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 2: Chess Piece Placements (mp3, 12min)

Candice Sands and Gaitrie Sackichand ask the question "In how many ways can you place two chess pieces on a chessboard so that they don't attack one another?". They investigate the king, rook, bishop, queen, and nightrider. Part of the interview is a discussion of teamwork in research. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 3: Chevron Tilings (mp3, 15min)

Varindra Hart counts square and domino tilings of a region composed of nested chevrons. Includes a surprise appearance by the square root of 17. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 4: Nurikabe (mp3, 8min)

Nikki investigates her favorite puzzle game Nurikabe, and asks how many 4x4 solvable Nurikabe boards exist. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 5: Lattice Paths (mp3, 6min)

Jan Bazant asks the question "How many lattice paths are there from (0,0) to (m,n) where each step can be North, East, or West?". He addresses the trials he faced throughout his research. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 6: Basketball (mp3, 10min)

Seung Park asks "In how many ways can the New York Knicks shoot the basketball?". He explains how he uses generating functions to answer this question. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 7: Dominosa (mp3, 20min)

Connie Durso and Davida investigate the game Dominosa. They count the number of possible ways to place dominoes on boards of different sizes before researching the number of possible valid Dominosa boards. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 8: Cycle Graphs (mp3, 11min)

Annette Paciorek investigates graphs that have the same degree sequence, focusing mainly on cycle graphs and when one additional edge is added. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 9: Monopoly (mp3, 9min)

Alex Yaroslavskiy likes board games and focused his research on the classic game Monopoly. He counts the number of ways to land on Boardwalk before passing Go and without landing in jail. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 10: Triangles (mp3, 11min)

Shao Xin is interested in polygons with integer vertex coordinates. He counts the number of triangles that have vertices somewhere on an nxn square grid. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 11: Growing Children (mp3, 11min)

Hanying Dong is interested in the factors that contribute to the growth of children. He uses generating functions to count the number of ways in which children can grow from ages 3 to 13. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 12: Walking Paths (mp3, 8min)

Yidi Yao takes inspiration from a walk in Manhattan; she counts the number of walking paths from one corner of a city to the other that do not pass through a park along the way. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 13: Go (mp3, 20min)

InSu Chang is interested in the game Go, which has simple rules but is both mentally challenging and mathematically complex. He answers a question about the end game possibilities when playing Go on a 5x5 board. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 14: Hallway Tiles (mp3, 8min)

Synthia Viaud noticed the patterns involved in the tiles on the hallway floor, and asks about the number of ways in which a person can walk around a closed square hallway respecting certain rules about walking on hallway tiles. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.

Episode 15: Stable Marriages (mp3, 7min)

Elisse Ferraro investigates the structure of stable marriages by using the Gale-Shapely algorithm. This research was conducted during Fall 2014 in Professor Hanusa's Combinatorics class.