The iOS game “Curiosity — What’s Inside the Cube?” presents an enormous cube composed of billions of minicubes that you can chip away, earning money to buy tools to, you guessed it, chip away minicubes more quickly. This “social experiment” promises to give the person who chips away the very last minicube a “life changing” discovery.
So how big is this cube? Yesterday (12/15/2012), my daughter and I happened to witness a layer being removed, with a new layer being composed of about 90,000,000 minicubes (available in the statistics icon in the game store). Assuming:
- That each side has the same number of minicubes
- That each side is a perfect square
- The edge minicubes are not shared between sides (probably easier to code)
- That the inner-most layer is 1 single minicube, the second layer has a faces that are 3x3, the third layer has faces that are 5x5, and so on
then the length of the cube edge is sqrt(90,000,000/6) or about 3873 minicubes. From the last assumption, that means we have about 3873/2 = 1936.2 layers left. At the time, 101 layers were removed, and when a new layer is revealed minicubes are removed very quickly (there are thousands of people clicking away at once), so this is probably a slight underestimate. Knowing experienced developers’ powers of two, the minicube probably started at 2048 layers.
The latest layers have been removed at a rate of one layer every 8 hours (available from the “Statistics PLUS” option in the game) or about 90,000,000*4 = 360,000,000 cubes per day. Today there were 103 layers removed. With 2048-103 = 1934 layers (and using a spreadsheet) there are 5.79 * 10^10 cubes left, which will take about 160 days to remove.
I had to make many assumptions here, but my current guess is that the secret will be revealed May 25, 2013 at the current rate.
I am most uncomfortable with fourth assumption (that the faces have the pattern 1, 3x3, 5x5, 7x7,…). If the layer faces instead follow the pattern 1, 2x2, 3x3, 4x4,… then the cube had about 4000 layers, we have 322 days left, and the last cube will be revealed on November 3rd, 2013.