UA-UMO 2005 Problem 102

Is it possible to divide a $10 \times 10$ board into:

$(a)$ $4$ figures of type $1$ and $21$ figures of type $2$ ? $(b)$ $4$ figures of type $1$ , $19$ figures of type $2$ , and $2$ figures of type $3$ ?

Attachments:

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.