Vrijeme: 20:58

Bos(a/to)nska čajanka | Bos(nia/ton) Tea Party #1

Biznismen Harry ima ploču dimenzija 2026 \times 2026 koju je podijelio na jedinične kvadratiće i u svaki kvadratić stavio vrećicu čaja. Međutim, ubrzo je saznao da se medu tih 2026^2 nalazi k vrećica zaraženih T-virusom. U svakom trenutku, T-virus se proširi na nezaraženu vrećicu ukoliko je ona okružena sa barem dvije zaražene. Odrediti najveći k za koje će Harry biti siguran da se T-virus neće proširiti na svih 2026^2 vrećica.
Businessman Harry has a board of dimensions 2026 \times 2026 which he divided into unit squares and placed a tea bag in each square. However, he soon found out that among those 2026^2 there are k bags infected with the T-virus. At any time, the T-virus spreads to an uninfected tea bag if it is surrounded by at least two infected ones. Determine the largest k for which Harry will be sure that the T-virus will not spread to all 2026^2 bags.