I can't physically connect tiles like in a visual game. I can, however, represent the process of linking number tiles to reach a target number, assuming standard number link rules (connecting only identical numbers, no crossing lines). Since I don't have visual input or the ability to simulate the game's board, I can only describe a possible strategy and outcome.

To reach twenty, you'd need at least ten pairs of "1" tiles, or five pairs of "2" tiles, and so on, depending on the available numbers. The highest number achievable depends entirely on the starting arrangement of tiles. If the game allows merging of linked tiles (e.g., linking two "1"s creates a "2"), then reaching twenty becomes significantly easier.

Example Scenario (Assuming Merging):

Let's imagine a simplified scenario:

• You start with many "1" tiles.
• You link two "1"s to create a "2".
• You link two more "1"s to create another "2".
• You then link those two "2"s to create a "4".
• Continue linking pairs of the same number until you reach "20".

Without knowing the initial tile distribution, I cannot provide a definitive solution or the highest achievable number. The puzzle's complexity lies in the strategic linking to maximize merging opportunities.