The weekend challenges can be solved without wasting points until Monday 11:59:59pm (CET). For more information see the rules of the game.
Enjoy the puzzle!
Project: 4TU.AMI
Challenge:
Elf Kubo and Ruprecht play a game with N ≥ 4 wooden cubes. At the beginning of the game, all six faces of each of these N cubes are empty and unlabeled.
In the first phase of the game, the two players label the 6N faces of the cubes with integers from the range 1, 2, … , N. In every move, exactly one face of one cube is labeled. They take turns at moving with Ruprecht making the first move.
In the second phase of the game, they build a tower from the \( N \) wooden cubes. The first (and bottom-most) cube in the tower must carry the integer 1 on one of its faces, the second one the integer 2, the third cube the integer 3, and so on. Ruprecht and Kubo take turns at choosing a cube with Ruprecht picking the first (and hence bottom-most) cube in the tower. The game ends only if in the k-th move there is no cube with integer k available.
Ruprecht wins the game if at the end of the game the tower consists of all N cubes. Otherwise, Kubo is the winner. During both phases of the game, Kubo and Ruprecht always make the best possible moves.
For which values of N with 4 ≤ N ≤ 7 can Ruprecht enforce a win?
Artwork: Julia Nurit SchÃ¶nnagel
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Possible answers: