1. At the beginning, there are 111 pieces of clay of equal weight on the table. Perform the following operations on the clay: First, divide a part or all of the clay into several groups, with the same number of pieces in each group, then knead the clay in each group into one piece. It is known that after $m$ operations, there are exactly 11 pieces of clay with different weights on the table. Find the minimum value of $m$.
1. 2 .

Obviously, one operation can result in at most two different weights of clay blocks.
Below, we show that two operations can achieve the goal.
Assume without loss of generality that each block of clay initially weighs 1.
In the first operation, select 74 blocks and divide them into 37 groups, with two blocks in each group. After the first operation, there are 37 blocks weighing 1 and 37 blocks weighing 2 on the table.

In the second operation, select 36 blocks weighing 1 and 36 blocks weighing 2, and divide them into 9 groups, with 8 blocks in each group. Specifically, the $i$-th group ($1 \leqslant i \leqslant 9$) contains $i-1$ blocks weighing 2 and $9-i$ blocks weighing 1. After the second operation, there are 11 blocks of clay on the table, with weights
$$
1, 2, 9-i+2(i-1)=7+i \quad (1 \leqslant i \leqslant 9).
$$

This meets the requirement.