Cube (algebra) the last two digits, "any" pair of digits with the last digit odd can be a perfect cube. With even cubes, there is considerable restriction, for only 00, 2, 4, 6 and 8 can be the last two digits of a perfect cube (where stands for any odd digit and for any even digit). Some cube numbers are also square numbers; for example, 64 is a square number and a cube number . This happens if and only if the number is a perfect sixth power (in this case 2). The last digits of each 3rd power are: It is,
Prince Rupert's cube this question in "Scientific American", Kay R. Pechenick DeVicci and several other readers showed that the answer for the (3,4) case is the square root of the smaller of two real roots of the polynomial formula_7, which works out to approximately 1.007435. For formula_8, the optimal side length of the largest square in an formula_5-dimensional hypercube is either formula_10 or formula_11, depending on whether formula_5 is even or odd respectively. Prince Rupert's cube In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube,