Statement

Giorgio, a notorious board game aficionado, has recently discovered an ancient board of the game of the goose, dating back to the late middle ages. The board is quite simple: a sequence of N cells (numbered from 0 to N-1), each of them granting a forward jump of J_i cells (possibly no jump, if J_i = 0). Players start at cell 0, then take turns in rolling a single six-sided die. Each player moves forward by the amount shown on the die rolled, then takes any jump granted by the landing cell (and possibly further jumps, if the cell reached after the jump allows it). The first player to go past cell N-1 wins the game. Giorgio is eager to try his new game, and so invited Edoardo to test it! Given that Giorgio has a strong preference for winning games, he plans to play with one of his rigged dice. The only question is, which one? Giorgio has six different rigged dice, numbered from 1 to 6, so that die i always lands on face i when rolled...