20 Jul
2012
20 Jul
'12
2:51 p.m.
It's difficult to enumerate disk polyominoes, because it's hard to recognize them. To illustrate this, I present a modest puzzle. I will give a set of lattice points. Either find a circular disk that covers these lattice points and no others, or prove that no such disk exists.
Here is the set. I am abbreviating (x,y) to the two-digit code xy.
01 02 03 04 11 12 13 14 20 21 22 23 24 25 31 32 33 34 35 42 43 44.
No disc exists. The presence of (0,1) and absence of (4,1) implies that the centre lies to the left of x = 2, whereas the presence of (3,5) and absence of (1,5) implies that it lies to the right of x = 2. Sincerely, Adam P. Goucher