The Gold Grabbing Game Gold Grabbing on Paths Gold Grabbing on - PowerPoint PPT Presentation

The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules The Gold Grabbing Game Gold Grabbing on Paths Gold Grabbing on Trees Deborah E. Seacrest Lemma Joint Work with Tyler Seacrest Theorem References May 2011

❼ ❼ Rules of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ A tree has (integer) amounts of gold at each vertex Gold Grabbing on Paths Gold Grabbing on Trees Lemma Theorem References

❼ ❼ Rules of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ A tree has (integer) amounts of gold at each vertex (and an Gold Grabbing on Paths even number of vertices). Gold Grabbing on Trees Lemma Theorem References

❼ Rules of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ A tree has (integer) amounts of gold at each vertex (and an Gold Grabbing on Paths even number of vertices). Gold Grabbing on ❼ Alice moves when there is an even number of vertices left and Trees Lemma Bob moves when there is an odd number. Theorem References

Rules of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ A tree has (integer) amounts of gold at each vertex (and an Gold Grabbing on Paths even number of vertices). Gold Grabbing on ❼ Alice moves when there is an even number of vertices left and Trees Lemma Bob moves when there is an odd number. Theorem ❼ On each turn, a player removes a leaf and adds the associated References amount of gold to his or her score.

❼ ❼ Advantages of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ First developed (on a path) at 1996 International Olympiad in Gold Grabbing on Paths Informatics Gold Grabbing on Trees Lemma Theorem References

❼ Advantages of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ First developed (on a path) at 1996 International Olympiad in Gold Grabbing on Paths Informatics Gold Grabbing on ❼ David Ginat used this as a game (on a path) to teach college Trees Lemma mathematics and computer science Theorem References

Advantages of the Game The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules ❼ First developed (on a path) at 1996 International Olympiad in Gold Grabbing on Paths Informatics Gold Grabbing on ❼ David Ginat used this as a game (on a path) to teach college Trees Lemma mathematics and computer science Theorem ❼ Can be used at a variety of levels and with “mis-matched” References opponents

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: Bob: References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 Bob: References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 Bob: 9 References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 + 4 Bob: 9 References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 + 4 Bob: 9 + 8 References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 + 4 + 7 Bob: 9 + 8 References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 5 + 4 + 7 Bob: 9 + 8 + 1 References

Greedy Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 16 Bob: 18 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: Bob: References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 Bob: References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 Bob: 8 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 Bob: 8 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 Bob: 8 + 1 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 + 99 Bob: 8 + 1 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 + 99 Bob: 8 + 1 + 5 References

Greedy Gold Grabbing on a Path Can Backfire The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 99 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 110 Bob: 14 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: Bob: References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: Bob: References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 Bob: References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 Bob: 8 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 Bob: 8 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 Bob: 8 + 5 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 + 9 Bob: 8 + 5 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 4 + 7 + 9 Bob: 8 + 5 + 1 References

Clever Gold Grabbing on a Path The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 4 8 7 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice: 20 Bob: 14 References

Why n Must Be Even The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest Rules Gold Grabbing on 5 1 4 1 9 5 Paths Gold Grabbing on Trees Lemma Theorem Alice wins Bob wins References

Extending to a Tree The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest 7 3 Rules Gold Grabbing on 4 1 6 Paths Gold Grabbing on Trees Lemma Theorem References 9 2 5 4 Alice: Bob: 8

Extending to a Tree The Gold Grabbing Game Deborah E. Seacrest Joint Work with Tyler Seacrest 7 3 Rules Gold Grabbing on 4 1 6 Paths Gold Grabbing on Trees Lemma Theorem References 9 2 5 4 Alice: 8 Bob: 8