The eight corner cubes of the black cube formed in
Paint it black (the cubes with half their faces already painted black) are assembled randomly into a smaller cube, with the outside of the new cube once again being painted black.
The eight cubes are then, again, disassembled and rebuilt randomly.
What is the probability that the outside of this cube is again completely black?
Bonus: What would the probability be if the smaller cube of eight cubes were a random selection of any eight cubes from the original black cube instead of only the eight corner cubes?
The required probability is (27/64)^8 = 282429536481/281474976710656 or about 0.001003391277553333793548517860472 or 1 in 996.620184339649558935041985666275374.
Bonus Solution
The required probability is 247324600785879/4628855992006737920, or
0.0000534310424029106 which is 1 in 18715.7119724380656633462.
Edited on February 14, 2024, 2:19 am
Puzzle Answer
