Artist Christine paints a 30cm white cube blue on all sides. She then cuts the cube into smaller cubes of dimension 10cm, collects and throws them up so that they land randomly onto the floor. What is the probability that all the top facing surfaces are blue?
Answer: This is as close as we have ever been to a trick question: the probability being zero, as the central cube will remain uncoloured. Not caught out, in order of reply, were: John Bowen, consultant, Bromsgrove, UK: Andrew Knox, Rubbond International, Ohé en Laak, The Netherlands; Michele Girardi, Scame Mastaf Spa, Suisio, Italy; Jose Padron, material development specialist, Waterville TG Inc., Waterville, Québec, Canada; David Mann, key account manager, SPC Rubber Compounding, UK; Daniel Willrich, redakteur, AutoRäderReifen-Gummibereifung, Hannover, Germany; Vivian Zhou, senior business development & market intelligence analyst. BU RE PLT APAC, Continental Tires (Shanghai) Co. Ltd, Shanghai, China; Stephan Paischer, head of product management special products, Semperit AG Holding, Vienna, Austria.
David Mann: As the cube from the centre of the original cube will be white on all sides, the probability is zero isn’t it? If you flip the question and estimate the probability of them all being white, it’s something like 1.008 x 10^-5. If you toss away the central cube than the probability of all the others being blue is 1.57 x 10^-15.
Jose Padron: The divided cube give 27 small cubes, with 162 faces. There are 54 blue faces: 8 cubes with three painted surfaces; thus, 8*3 = 24 blue sides out of 8*6 = 48 total sides; 12 cubes with two painted surfaces. Thus, 12*2 = 24 blue sides out of 12*6 = 72 total sides
6 cubes with one painted surface; thus, 6*1 = 6 blue sides out of 6*6 = 36 total sides However, there is; one cube with no painted surfaces. The core of the original cube was not painted.
Unless you are an avid reader of ERJ back issues, it was rather difficult to guess the precise year of the article. Extra well done, so, to Stephan Paischer, Jose Padron, Andrew Knox who came in right on the money with 2014.
Try to guess the year-of-publication of the following snippet from the ERJ archives, which date back to 1884.