Combinatorial game theory

2 artículos

Combinatorics & Discrete Math GradoAnálisis10 min

The Coin in the Middle, and the Table Where It Fails

Take the centre, then mirror every move through it, and you place the last coin. The proof has three requirements and only one of them needs that opening move, which is the step a one-line answer skips. Central symmetry alone is not the condition: an annulus is centrally symmetric and the first player loses on it.

Combinatorics & Discrete Math BachilleratoExplicación9 min

Say Six: The Only Opening That Wins the Race to Fifty

Counting to fifty in steps of one to ten, the first player wins, and exactly one of the ten legal openings does it. The stations are 6, 17, 28, 39 and 50, spaced eleven apart because eleven is one more than the largest legal step. The article carries the residue argument that proves the opening is unique, and the target 55 where the advantage flips.