a.k.a. Genius Puzzle
(3 section, 6 column tower is 1.75" by 2.75" long with 5/8" tiles,
3 section, 6 column Genius tower is 1.75" by 2.8" long with 5/8" tiles,
3 section, 6 column keychain tower is 1.75" by 2.75" long with 3/4" tiles,
2 section, 6 column custom made tower is 1.75 inches by 2" long with 3/4" tiles
4 section, 6 column keychain tower is 1.25" by 3" long with 1/2" x 3/8" tiles,
4 section, 6 column keychain tower 2 is 1.25" by 2.25" long with 3/8" tiles,
6 section, 6 column tower is 2" by 4.75" long with 3/4" tiles)

These puzzles consist of a number of sections that can rotate; the puzzle is solved when each column has a single color. One color has one fewer tiles than the others, and this gap is what allows pieces to be moved around. Because all tiles of a given color are identical, solving is relatively easy; any tile can effectively be moved to any position without disturbing the others, with any assignment of colors to columns, one tile at a time (larger versions just take longer). When the number of number of sections and columns is the same, a second problem is to put the same color tile in each row.

When the number of number of rows and columns is the same, a second problem is to put the same color tile in each row.

Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tower.htm