164051

With seven cubes (1 and 6, 2 and 5, 3 and 4) and with six cubes (1 and 5, 2 and 4, 3 and 3), there are three possible solutions and with eight cubes, there are four resolutions. They are 1 and 7, 2 and 6, 3 and 5 and 4 and 4. For the answer for five cubes, I predicted two solutions (1 and 4, 2 and 3) and after working it out, I discovered that I was right. There are also ten way for 20 cubes. I have possibly found a pattern in how many solutions there are for every amount of cubes. For an even amount of cubes, there are half of that number of solutions. For example, take 50 cubes. You will most likely find that there are 25 solutions. Half of 50 is 25. WHen there is an odd number though, you half it and take away 0.5. Take 15. Half of that is 7.5. Take away 0.5 and you have seven solutions.