MultiplyDiscrete Mathematics Level 5
At \(t = 1\), all snowflakes which occupy the exact same points are merged into one, and then the process repeats for every snowflake, resulting in the following pattern:
So, to iterate the first few steps:
- There is \(1\) snowflake at time \(t = 0\)
- At time \(t = 1\), there are \(8\) snowflakes pre-merge.
- No snowflakes coincide, so there are \(8\) snowflakes post-merge as well.
- At time \(t = 2\), there are \(64\) snowflakes pre-merge.
- Post-merge, only \(33\) snowflakes remain.
How many snowflakes are there at time \(t = 1000\), post-merge?