# Polyominoes inside a 10x10 grid

Can you place five dominoes, five trominoes, five tetrominoes, five pentominoes and five hexominoes inside a 10x10 grid, such that:

• No two polyominoes overlap
• No two polyominoes of the same size (by area) touch each other orthogonally (horizontally or vertically)
• My previous puzzle was too easy so I made this one. Jun 18, 2022 at 23:33
• Maybe we should have a separate "XXominoes inside XxX grid" site. Jun 19, 2022 at 1:14

Unfortunately, this is also too easy.

This solution is trivial:

• I feel so stupid now. It took my program many hours to find a solution. Jun 19, 2022 at 2:08
• What if we disallow straight polyominoes (except dominoes), can it still be solved? Jun 19, 2022 at 2:10
• I did it without straight polyominoes (except dominoes). Jun 19, 2022 at 2:21
• @DmitryKamenetsky Don't feel bad. It can be hard to come up with good puzzles. Just a tip, though: computers usually aren't the best way to judge the difficulty of a puzzle. Computers don't have imaginations or experience, which are important tools for solving things. Humans, on the other hand, have both those traits. Jun 20, 2022 at 15:51

I can do it with no straight polyominoes (except dominoes):

An obvious upper bound for the maximum number of distinct shapes is $$1+2+5+5+5=18$$, and...

...this solution attains that upper bound:

• You could try to maximize the number of distinct polyominoes. Jun 19, 2022 at 1:57
• @DanielMathias Good suggestion. Done. Jun 19, 2022 at 2:25
• Nice, and with distinct fixed trominoes. Jun 19, 2022 at 2:41
• Very nice! You've solved every version of this problem :) Jun 19, 2022 at 3:23