In this document, I will set out to determine two values:

1. A lower bound on the number of unique Get Stars boards
2. A rough estimate of the amount of time to play every unique board

Get Stars takes place on a 10 by 10 grid. The player may start on any of the 10 * 10 = 100 cells.

Each barrier is 2 by 2 cells in size. There are 9 * 9 = 81 possible positions for each barrier. However, the barriers may not collide with the player, and must have at least 1 cell of space separating each other. As a worst-case scenario, the player will remove 2 * 2 = 4 possible positions for the first barrier. This means the first barrier has at least 81 - 4 = 77 possible positions. Each barrier removes 5 * 5 = 25 possible positions for the next barrier under the worst-case scenario. Therefore the second barrier has at least 77 - 25 = 52 possible positions, and the third barrier has 52 - 25 = 27 possible positions. This means there are at least 77 * 52 * 27 = 108,108 configurations of all three barriers.

Stars occupy 1 cell, and may not collide with any other entity. After the player and barriers have been placed, there are 100 - 1 - 3 * 4 = 87 available positions for stars. After each star is placed, there is one fewer available position for the next star. There are 10 stars total. Therefore the number of star configurations is 87 * 86 * 85 * 84 * 83 * 82 * 81 * 80 * 79 * 78 = 14,517,925,392,916,108,800.

Now we can obtain a lower bound on the number of unique Get Star boards. We will multiply the number of player positions by the number of barrier configurations by the number of star configurations. There are at least 100 * 108,108 * 14,517,925,392,916,108,800 = 156,950,387,837,737,469,015,040,000 unique Get Stars boards. In scientific notation, this number is 1.56 * 10^26. The name for this number is 156 septillion.

I timed myself clearing 10 boards, and it took 90 seconds. This means it takes 9 seconds to clear each board. This means it will take 9 * 156,950,387,837,737,469,015,040,000 = 1,412,553,490,539,637,221,135,360,000 seconds to clear every unique board. There are 60 * 60 * 24 * 365 * 1,000 = 31,536,000,000 seconds in a millennium. Therefore it will take 1,412,553,490,539,637,221,135,360,000 / 31,536,000,000 = 44,791,777,350,952,474 millennia to clear all unique boards. In scientific notation, this number is 4.47 * 10^16. The name for this number is 44 quadrillion.

You'd better start playing now.