I have a puzzle consisting of 100 (10x10) pieces.

What is the minimum number of pieces I have to draw randomly from a pile to be guaranteed that I can join them all together so that no piece is isolated (i.e. not joined to any other piece)?

**Details and Assumptions:**

Every piece is equally likely to be picked. I don't look whether the first piece has a straight edge or similar tricks.

Every piece only fits together with its neighboring pieces, and there is a unique solution to the puzzle.

Two pieces that only share a corner are not considered "joined."