Players Aino and Eino take turns choosing numbers from the set {0,...,n} with nāN being fixed in advance.
The game ends when the numbers picked by one of the players include an arithmetic progression of length 4.
The one who obtains the progression wins.
Prove that for some n, the starter of the game wins. Find the smallest such n. symmetryarithmetic sequencecombinatorics unsolvedcombinatorics