Question 5
Initially the number $10$ is written on the board. In each subsequent move, you can either (i) erase the number $1$ and replace it with a $10$, or (ii) erase the number $10$ and replace it with a $1$ and a $25$, or (iii) erase a $25$ and replace it with two $10$s. After some time, you notice that there are exactly one hundred copies of $1$ on the board. What is the least possible sum of all the numbers on the board at that moment?