In which board game do players use a ‘doubling cube’, which has the numbers 2,4,8,16,32,64 on it?
Backgammon not a die to be rolled but rather a marker with the numbers 2, 4, 8, 16, 32, and 64 inscribed on its sides, to denote the current stake. At the start of each game, the doubling cube is placed on the bar with the number 64 showing; the cube is then said to be "centered, on 1". When the cube is centered, the player about to roll may propose that the game be played for twice the current stakes. Their opponent must either accept ("take") the doubled stakes or resign ("drop") the game immediately. Whenever a player accepts doubled
Doubling the cube at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, . This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that is not a constructible