Dillon Mayhew

1. Outreach experiences as a Bevan Werry Speaker Dillon Mayhew

2. My background I teach mathematics at Victoria University of Wellington.My research is in a branch of mathematics called matroid theory, which is the study of abstract geometrical configurations.

3. My background I have been running outreach activities around Wellington for several years. In 2013 and 2014, the Bevan Werry speakership allowed me to run workshops around the country.

4. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

5. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

6. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

7. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

8. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

9. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

10. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

11. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

12. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

13. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

14. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

15. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

16. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

17. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

18. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

19. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

20. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

21. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

22. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

23. The game of subtraction • Start from a positive integer. • Take turns to subtract either 1, 2, or 3. • The player who arrives at zero wins.

24. Combinatorial games This is an example of an acyclic directed graph. Impartial games are played on graphs like these. A sink is a node in the graph with no departing arrows. We take turns moving along arrows of the graph. The player who arrives at a sink wins.

25. Grundy’s game • Start with a pile of n stones. • On each turn, divide a pile into two smaller piles, of unequal sizes. • If a player cannot divide any of the piles, they lose.

26. Grundy’s game • Start with a pile of n stones. • On each turn, divide a pile into two smaller piles, of unequal sizes. • If a player cannot divide any of the piles, they lose.

27. Grundy’s game • Start with a pile of n stones. • On each turn, divide a pile into two smaller piles, of unequal sizes. • If a player cannot divide any of the piles, they lose.

28. Grundy’s game • Start with a pile of n stones. • On each turn, divide a pile into two smaller piles, of unequal sizes. • If a player cannot divide any of the piles, they lose.

29. Grundy’s game • Start with a pile of n stones. • On each turn, divide a pile into two smaller piles, of unequal sizes. • If a player cannot divide any of the piles, they lose. • If we start with 3 stones, the number assigned to the starting position is 1. • If we start with 4 stones, the number assigned to the starting position is 0.If we start with 5 stones, the number assigned to the starting position is 2. • If we start with 6 stones, the number assigned to the starting position is 1. • This sequence starts with 102 102 10 2 1 3 2 1 3 2 4 3 0…

30. Grundy’s game This sequence starts with 102 102 10 2 1 3 2 1 3 2 4 3 0… Nobody knows if this sequence eventually starts repeating itself!This problem has been open for 35 years.The first values of the sequence have been calculated, but we still have not seen a repeating pattern.