This question is aimed at people who have a really good grasp of standard Slitherlink puzzles.
This is a standard, square cell, 10x10 Slitherlink puzzle I designed. It isn't what I would call a "true" Slitherlink puzzle, though.
A true Slitherlink puzzle has as its solution exactly one closed, non-intersecting "loop" that goes along the grid lines between the numbers, and satisfies the numbers in the cells: each number has the loop bordering its square on exactly that many sides. It may surprise you to find out that this puzzle can become a true Slitherlink puzzle by removing some of the "2"s from the board.
What is the least number of twos that need to be removed in order for this Slitherlink to have exactly one solution? Anybody could stumble upon the answer, so if you post an answer below, you must explain why it cannot be less than the number you found.
The above image was taken from this website which contains a powerful SAT solver for Slitherlink puzzles. I consider it fair to use such a solver for this question, but you still have to explain what is going on.
There are more questions I can ask on the topic of Slitherlink puzzles made just from twos, so if there is interest... there's more where this came from.