4
$\begingroup$

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)
Improve this question
$\endgroup$
2
  • $\begingroup$ My previous puzzle was too easy so I made this one. $\endgroup$ Commented Jun 18, 2022 at 23:33
  • 3
    $\begingroup$ Maybe we should have a separate "XXominoes inside XxX grid" site. $\endgroup$ Commented Jun 19, 2022 at 1:14

2 Answers 2

Reset to default
6
$\begingroup$

Unfortunately, this is also too easy.

This solution is trivial:

enter image description here

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ I feel so stupid now. It took my program many hours to find a solution. $\endgroup$ Commented Jun 19, 2022 at 2:08
  • $\begingroup$ What if we disallow straight polyominoes (except dominoes), can it still be solved? $\endgroup$ Commented Jun 19, 2022 at 2:10
  • 4
    $\begingroup$ I did it without straight polyominoes (except dominoes). $\endgroup$ Commented Jun 19, 2022 at 2:21
  • 3
    $\begingroup$ @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. $\endgroup$ Commented Jun 20, 2022 at 15:51
6
$\begingroup$

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

enter image description here

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: enter image description here

Improve this answer
$\endgroup$
4
  • $\begingroup$ You could try to maximize the number of distinct polyominoes. $\endgroup$ Commented Jun 19, 2022 at 1:57
  • $\begingroup$ @DanielMathias Good suggestion. Done. $\endgroup$ Commented Jun 19, 2022 at 2:25
  • 2
    $\begingroup$ Nice, and with distinct fixed trominoes. $\endgroup$ Commented Jun 19, 2022 at 2:41
  • $\begingroup$ Very nice! You've solved every version of this problem :) $\endgroup$ Commented Jun 19, 2022 at 3:23

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.