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

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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

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

The Gold Grabbing Game

Deborah E. Seacrest Joint Work with Tyler Seacrest May 2011

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

Rules of the Game

❼ A tree has (integer) amounts of gold at each vertex ❼ ❼

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

Rules of the Game

❼ A tree has (integer) amounts of gold at each vertex (and an

even number of vertices).

❼ ❼

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

Rules of the Game

❼ A tree has (integer) amounts of gold at each vertex (and an

even number of vertices).

❼ Alice moves when there is an even number of vertices left and

Bob moves when there is an odd number.

❼

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

Rules of the Game

❼ A tree has (integer) amounts of gold at each vertex (and an

even number of vertices).

❼ Alice moves when there is an even number of vertices left and

Bob moves when there is an odd number.

❼ On each turn, a player removes a leaf and adds the associated

amount of gold to his or her score.

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

Advantages of the Game

❼ First developed (on a path) at 1996 International Olympiad in

Informatics

❼ ❼

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

Advantages of the Game

❼ First developed (on a path) at 1996 International Olympiad in

Informatics

❼ David Ginat used this as a game (on a path) to teach college

mathematics and computer science

❼

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

Advantages of the Game

❼ First developed (on a path) at 1996 International Olympiad in

Informatics

❼ David Ginat used this as a game (on a path) to teach college

mathematics and computer science

❼ Can be used at a variety of levels and with “mis-matched”

pponents

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: Bob:

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 Bob:

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 Bob: 9

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 + 4 Bob: 9

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 + 4 Bob: 9 + 8

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 + 4 + 7 Bob: 9 + 8

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 5 + 4 + 7 Bob: 9 + 8 + 1

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

Greedy Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 16 Bob: 18

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: Bob:

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 Bob:

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 Bob: 8

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 + 7 Bob: 8

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 + 7 Bob: 8 + 1

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 + 7 + 99 Bob: 8 + 1

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 4 + 7 + 99 Bob: 8 + 1 + 5

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

Greedy Gold Grabbing on a Path Can Backfire

4 8 7 1 99 5 Alice: 110 Bob: 14

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: Bob:

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: Bob:

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 Bob:

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 Bob: 8

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 + 7 Bob: 8

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 + 7 Bob: 8 + 5

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 + 7 + 9 Bob: 8 + 5

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 4 + 7 + 9 Bob: 8 + 5 + 1

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

Clever Gold Grabbing on a Path

4 8 7 1 9 5 Alice: 20 Bob: 14

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

Why n Must Be Even

5 1 4 1 9 5 Alice wins Bob wins

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: Bob:

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 8 Bob:

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 8 Bob: 7

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 14 Bob: 7

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 14 Bob: 11

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 19 Bob: 11

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 19 Bob: 15

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 28 Bob: 15

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 28 Bob: 18

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 30 Bob: 18

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

Extending to a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 30 Bob: 19

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

Past Work

Theorem (Micek and Walczak, 2010) If T is a tree with an even number of vertices, Alice can secure at least one-fourth of the gold.

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

Past Work

Theorem (Micek and Walczak, 2010) If T is a tree with an even number of vertices, Alice can secure at least one-fourth of the gold. Conjecture (Micek and Walczak, 2010) If T is a tree with an even number of vertices, Alice can secure at least half the gold.

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

Theorem

Theorem If T is a tree with an even number of vertices, Alice can secure at least half the gold.

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

Rooted and Non-rooted Gold Grabbing on a Tree

4 9 2 5 4 8 6 1 7 3 Alice: Bob:

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

Rooted and Non-rooted Gold Grabbing on a Tree

4 9 2 5 4 8 6 1 7 3 Alice: Bob:

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

Rooted and Non-rooted Gold Grabbing on a Tree

4 9 2 5 4 8 6 1 7 3 Alice: 7 + 1 Bob: 3 + 2

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

Rooted and Non-rooted Gold Grabbing on a Tree

2 1 7 3 Alice: Bob:

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

Rooted and Non-rooted Gold Grabbing on a Tree

2 1 7 3 Alice: 7 + 2 Bob: 3 + 1

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game.

❼ ❼ ❼ ❼ ❼ ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ ❼ ❼ ❼ ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ True for n ≤ 3. ❼ ❼ ❼ ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ True for n ≤ 3. ❼ True when Alice moves first. ❼ ❼ ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ True for n ≤ 3. ❼ True when Alice moves first. ❼ True when Bob’s optimal first move (in the non-rooted game)

isn’t the root.

❼ ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ True for n ≤ 3. ❼ True when Alice moves first. ❼ True when Bob’s optimal first move (in the non-rooted game)

isn’t the root.

❼ True when the root is adjacent to vertex u of degree 2. ❼

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

Lemma

Lemma For Alice, the non-rooted game on any number of vertices is at least as good as the rooted game. Proof.

❼ Induct on the number of vertices. ❼ True for n ≤ 3. ❼ True when Alice moves first. ❼ True when Bob’s optimal first move (in the non-rooted game)

isn’t the root.

❼ True when the root is adjacent to vertex u of degree 2. ❼ True otherwise.

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold.

❼ ❼ ❼

❼

❼ ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ ❼

❼

❼ ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼

❼

❼ ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼

❼ ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼ By choosing between the games, Alice can win or tie.

❼ ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼ By choosing between the games, Alice can win or tie.

❼ Game 1: equivalent to playing on T rooted at v. ❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼ By choosing between the games, Alice can win or tie.

❼ Game 1: equivalent to playing on T rooted at v. By lemma,

playing non-rooted is at least as good.

❼

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼ By choosing between the games, Alice can win or tie.

❼ Game 1: equivalent to playing on T rooted at v. By lemma,

playing non-rooted is at least as good.

❼ Game 2: equivalent to her taking v and then playing on T ′

rooted at u.

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

Theorem

Theorem If T has an even number of vertices, Alice can secure at least half the gold. Proof.

❼ Let v be any leaf, u the neighbor of v, and T ′ = T − v. ❼ Game 1: Alice goes first on T ′ rooted at u. Bob gets v. ❼ Game 2: Alice gets v and goes second on T ′ rooted at u.

❼ By choosing between the games, Alice can win or tie.

❼ Game 1: equivalent to playing on T rooted at v. By lemma,

playing non-rooted is at least as good.

❼ Game 2: equivalent to her taking v and then playing on T ′

rooted at u. By lemma, playing non-rooted is at least as good.

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

Questions and Extensions

❼ What is Alice’s strategy? ❼

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

Questions and Extensions

❼ What is Alice’s strategy? ❼ What if a tree (or even a path) has an odd number of vertices?

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

References

Ginat, D. (2006). Winning moves and illuminating mathematical

patterns. Mathematics and Computer Education, 40(1), 42–50.

Micek, P., and Walczak, B. Parity in graph sharing games. Available at: http://tcs.uj.edu.pl/~walczak/graph-sharing.pdf Rosenfeld, M. A gold-grabbing game. Available at: http://garden.irmacs.sfu.ca/?q=op/a_gold_grabbing_game

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

E-mail Address

debbie.seacrest@gmail.com