# Azure

 13 Reputation 21 views

## Registered User

 Name Azure Member for 4 months Seen Jan 11 at 0:00 Website Location Age
 Jan9 awarded ● Scholar Jan9 awarded ● Student Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz In retrospect, my question was atrociously worded. Hopefully I have made it clearer. Jan9 revised Minimizing the Perimeter of a polyominoadded 8 characters in body; added 1 characters in body Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz At no point does one try to fit or nest together assemblies of more than one unit square. Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz Oh! I meant, I will give you $N$ copies of unit squares, and you make one polyomino, and try to minimize the number of "free" unit square sides. Jan9 comment Minimizing the Perimeter of a polyomino$Aaron Meyerowitz For example, a simple cross with tiles at {{0,0},{1,0},{0,1},{-1,0},{0,-1}} would have 12 "free" sides, whereas one could approximate a rectangle with tiles at: {{0,0},{0,1},{1,0},{1,1},{1,2}} that only has 10 "free" sides. Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz This is very interesting to read. However, my intention was to ask about a polyomino construction and to refer to "sides" as the sides of the squares composing the polyomino. Jan9 awarded ● Editor Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz I have added to the problem description. Please let me know if you think my question is still underspecified. Jan9 revised Minimizing the Perimeter of a polyominoadded 290 characters in body Jan9 comment Minimizing the Perimeter of a polyomino@Aaron Meyerowitz You are given$N$tiles, and you can make a tiling as you wish with them. You don't have to necessarily make a rectangle, you just need to minimize the number of edges where some$(N+1)th\$ tile can be placed. Jan9 asked Minimizing the Perimeter of a polyomino