**SEXTILLIONS*** (1 to 6 players)*

This new release from the company that makes Quintillions (see The Games 100, November 1984) offers, as is usual for Kadon, some handsome equipment that may be used for both strategy games and solitaire puzzles. The 36 laser-cut acrylic pieces constitute the complete set of 35 "hexominoes" — shapes that can be formed by joining six squares along their edges — plus one extra tile (the mirror image of one of the other 35), which among other things makes it possible to divide the tiles equally between two players. These 36 tiles — or "Sextillions" — are colored to form groups of 24 "equal" and 12 "unequal" pieces, depending on whether or not they cover equal numbers of light and dark squares when placed on a checkerboard.
Rules are included for four competitive games, three of which are played on a vinyl board with a 15x15 grid. "Cornered" is played much like the classic game of Pentominoes: One player uses the equal pieces, the other the unequal pieces, and the players take turns placing them on the board until one player — the loser — is forced to place a tile next to another one. "Sidestep" is a very short connection game in which players have differing objectives. (They also have unequal winning chances, but the game is interesting despite this flaw.) The game we liked best is "1-2-3-4," in which two players divide up both the equal and unequal sets of tiles, and then take turns placing their equal pieces on the board. The goal is to leave vacant areas in which one's own unequal pieces will fit, but not the opponent's. The game is a very demanding test of strategic ability and spatial perception, although closely matched players may find that ties are common. The final game, "Sextillions," patterned after the game Quintillions, also tests one's ability to visualize shape patterns. As many as six players try first to place tiles on a flat surface, and then to rearrange them so that as much of each tile's perimeter as possible borders other tiles.

The puzzles, of which there are over 180, involve forming rectangles and other shapes by piecing together various numbers of Sextillions. The most fascinating challenge is the set of 34 "Progressions." These begin with an arrangement of three tiles into a 3x6 rectangle, to which you are asked to add a fourth specified piece to produce a 4x6 rectangle — a task that requires you to rearrange the original three pieces. One piece at a time is added in this way to produce larger and larger rectangles, until all 36 tiles are fit together. Once you get past the first three or four problems in the set, the going really gets tough.

Sextillions is especially recommended for people who enjoy geometric puzzles and games. But the difficulty level of the puzzles is varied enough, as is the nature of the play, for the game to appeal to a wide audience. —R.W.S.