A snake is a series of unit length matches, laid head to tail at multiples of 30 degrees, never touching other matches. How big of a snake can be in a side-2 square? Oyvind Tafjord let a program run for a few days, and it give some interesting results. It turns out there are two length-20 snakes. {{1, 3, 10, 7, 7, 4, 4, 1, 8, 1, 10, 5, 10, 5, 10, 1, 3, 5, 12, 9}, {1, 4, 9, 7, 4, 11, 4, 11, 4, 2, 10, 10, 7, 7, 4, 4, 1, 10, 5, 10}} You can think of these numbers as a series of clockface headings. There are 64 length-19 snakes. I give them here in doudecimal. 114477A31A5A5901496, 114477A31A703A76307, 114477A3A3A703A3470, 114477A3A30707075A1, 114477A307A3A3A3470, 114477A30703A7075A1, 114477A30A5A5A13470, 114477AB2494941BA72, 114477AB272B4727941, 114477AB274B4B4BA72, 114477AB4B272727941, 114477BB4B472BA764B, 11447708B418181461A, 1146277A318A3A3A753, 1162477AB164B4B479B, 1347B692B69114477A3, 1349692B69114477A31, 1349692B69114477A30, 13A7734941196B29691, 13A7734941196B29692, 13A774411892964B418, 13A77441196B2969430, 13A77441199494169A1, 13A7744181A5A5A1350, 1448727AA25092529B4, 14581A5A5511AA7735A, 1461AA7743A3A3A7074, 149470707427AA11449, 1494946BA5A11447A3A, 1494949427AA1144961, 1496169427AA1144961, 14969114477A3192969, 14969114477A31A5A59, 1496911447701969416, 149727272B4BA774418, 14974B4B42AA77441A5, 14974B4B42AA7744027, 14974B4B4727AA11449, 14974B4B40A77441A5A, 15692B69114477A30B4, 15692B69114470A5694, 1585038511A5AB774B2, 161467A3A3A3A707494, 161A774411970707427, 1625A5A83511A807722, 1663A3A05377A081166, 168303850377A3A9116, 168305830377AA1153A, 168305058511AA7735A, 16843A3A05377AA1166, 1684411AA56B63181A5, 1684411AA636B6B8350, 1684411AA636B836B92, 169014961479411AA76, 21AA774B14949521A58, 21AA774B4B472B4BA72, 2478B4181884411AA72, 25A527AA11449A72529, 2727A5A03A3A7744118, 277AA1149614974B418, 27A5A0383277AA11538, 27AA11448B638B6A125, 27AA114947070742058, 2B477AA115830585AB2 These snakes are interesting creatures. I'm working on making scalable pictures of all of them. All of them have interesting properties. 15692B69114477A30B4, for example, goes in 11 of the 12 possible directions. I plan on looking at different angles, and different bounding shapes. --Ed Pegg Jr, www.mathpuzzle.com