The Cup Song, Logically
Anna is trying to stack 10 upside-down cups. She works to the plan that she will place one cup at a time and start from the bottom. Every time she places a cup, she will place the highest one possible (i.e. a cup higher up can be placed when when the 2 below it are placed). In this system, the first cup placed is 1 and the last is 10. When she has finished, she numbers the cups again from 1 to 10, 1 being the top row, 7-10 being the bottom (left to right). Based on these two numbering systems, at which cup will both numbers match?