OFFSET
1,1
COMMENTS
The only cases, currently known to the author, for which the maximum difficulty level is not an integer, are n = 7 (difficulty level 160/3) and n = 13 (difficulty level 8960/3).
EXAMPLE
The following table shows all sets of pieces that give the maximum (n,2)-tiling difficulty level up to n = 27.
\ Number of pieces of size
n \ 1X1 | 1X2 | 1X3 | 1X4 | 1X5 | 1X7 | 2X2 | 2X3
----+-----+-----+-----+-----+-----+-----+-----+----
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0
2 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 0
3 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0
4 | 0 | 2 | 0 | 1 | 0 | 0 | 0 | 0
4 | 0 | 1 | 2 | 0 | 0 | 0 | 0 | 0
5 | 1 | 2 | 0 | 0 | 1 | 0 | 0 | 0
5 | 0 | 3 | 0 | 1 | 0 | 0 | 0 | 0
6 | 0 | 1 | 2 | 1 | 0 | 0 | 0 | 0
7 | 0 | 1 | 4 | 0 | 0 | 0 | 0 | 0
8 | 2 | 0 | 2 | 1 | 0 | 0 | 1 | 0
8 | 0 | 1 | 2 | 1 | 0 | 0 | 1 | 0
9 | 1 | 0 | 3 | 2 | 0 | 0 | 0 | 0
10 | 2 | 0 | 2 | 1 | 0 | 0 | 2 | 0
11 | 1 | 0 | 3 | 2 | 0 | 0 | 1 | 0
12 | 1 | 0 | 3 | 2 | 0 | 0 | 0 | 1
12 | 0 | 0 | 4 | 3 | 0 | 0 | 0 | 0
13 | 1 | 0 | 3 | 2 | 0 | 0 | 2 | 0
14 | 0 | 0 | 4 | 3 | 0 | 0 | 1 | 0
15 | 0 | 0 | 4 | 3 | 0 | 0 | 0 | 1
16 | 0 | 0 | 4 | 3 | 0 | 0 | 2 | 0
17 | 0 | 0 | 4 | 3 | 0 | 0 | 1 | 1
18 | 0 | 0 | 4 | 3 | 0 | 0 | 0 | 2
19 | 0 | 0 | 4 | 3 | 0 | 0 | 2 | 1
20 | 0 | 0 | 4 | 3 | 0 | 0 | 1 | 2
21 | 0 | 0 | 4 | 3 | 0 | 0 | 0 | 3
22 | 0 | 0 | 5 | 2 | 0 | 1 | 2 | 1
22 | 0 | 0 | 5 | 0 | 3 | 0 | 2 | 1
22 | 0 | 0 | 4 | 3 | 0 | 0 | 2 | 2
23 | 0 | 0 | 5 | 2 | 0 | 1 | 1 | 2
23 | 0 | 0 | 5 | 0 | 3 | 0 | 1 | 2
23 | 0 | 0 | 4 | 3 | 0 | 0 | 1 | 3
24 | 0 | 0 | 5 | 2 | 0 | 1 | 0 | 3
24 | 0 | 0 | 5 | 0 | 3 | 0 | 0 | 3
24 | 0 | 0 | 4 | 3 | 0 | 0 | 0 | 4
25 | 0 | 0 | 3 | 4 | 0 | 1 | 0 | 3
26 | 0 | 0 | 5 | 2 | 0 | 1 | 1 | 3
26 | 0 | 0 | 5 | 0 | 3 | 0 | 1 | 3
27 | 0 | 0 | 5 | 2 | 0 | 1 | 0 | 4
27 | 0 | 0 | 5 | 0 | 3 | 0 | 0 | 4
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Mar 11 2023
STATUS
approved