I looked for the puzzle blocks, and found nothing.
You fell into the trap of designing your business cards but neglecting how the business would work.
This kind of puzzle relies on tables (lists of lists) and the Any (component) blocks.
You will need to code a table whose rows are the various aisles (I can't call them rows and columns because I already used some of those words for my internal data structures.)
You have 10 aisles, 5 vertical and 5 horizontal.
Because you chose a 5 by 5 puzzle, each aisle has 5 checkbox components in it, along with a Label component to show the desired count for that aisle.
That structure can be reused across puzzles at runtime.
A puzzle is defined by the 10 numbers reading across the top of the puzzle and down the left side. Those numbers are targets for the sum of the number of checked checkboxes in that matching aisle, right?
This foundation will make for a simpler app logic for you to code.
P.S. The AI2 Table Arrangement is notoriously buggy, and can corrupt AI2 projects if you have them in Designer Copy/Paste operations. I personally prefer nested Horizontal Arrangements inside a Vertical Arrangement. The Designer's Copy/Paste facility makes those easy to build.
Here are some sample projects to study ...