Épreuve de setion européenne
1 General knowledge
What do you know about onditional probabilities? Give a few formulas (you an
useaprobability tree).
2 Doument
The Game of Life was devised in 1970 by British mathematiian John Horton
Conway. Itisazero-player gametakingplaeina gridmadeofsquareellsthatan
be lled or empty. An empty ell is said to be dead, while a lled ell is said to be
alive or living.
The game starts with a set of living ells, the initial state. Eah ell will interat
with its 8 neighbours so that the status of eah ell in the grid may hange when
movingtothe nextstep(ornextgeneration).Birthsanddeathsourfollowing four
preiserules.
1. Aliving ell with exatlytwo or threeneighbours staysalive.
2. Aliving ell with lessthan two neighboursdies ofloneliness.
3. Aliving ell with more than threeneighbours diesof rowding.
4. Adead ell with exatlythree living neighbours omes to life.
Astill lifeisastatipattern,apatternthatdoesnothangefromonegeneration
to the next.
An osillator isa pattern that repeatsitself after a number of generations.This
number isalled theperiod of the osillator.
Adapted fromvarious soures.
3 Questions
1. Whodevised thisgame, and when?
2. Explainthe meaning of the senteneIt isazero-player game.
3. Find,amongthe following patterns, the still-lifes andthe osillators.
A B C D E
4. Aretherepatterns thatareneither still-lifes nor osillators?
