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I’ve recently (March 2013) devised an amusement using a set of 12 planar pentacubes. I call it “Pentacube Pile Up”, because basically you pile pentacubes up.  The object of the puzzle game is to score more points than your opponents, or more than your previous best score if you play it as a puzzle for one.  It will help develop social skills, basic numeracy, motor skills and spatial awareness. Larger sets of pentacubes are recommended. This game is ideal for anyone with a short little span of attention as the game only takes a few moments to complete.

Overview

Players take it in turns to place a planar pentacube onto the playing surface. The first two pieces are placed flat on the surface, touching each other corner to corner in a rectilinear fashion.  Play continues with each player in turn adding a pentacube at any level above the first two played. For each horizontal unit square under your just-played piece that touches a previous unit square, you score one point. For each vertical unit square that touches a previous unit square, you score two points.  Play continues until all 12 pieces have been played. The player with the highest number of points wins.

Left and right, the interesting, precarious structures which are created by the end of a game of “Pentacube Pile Up”

There may be real or perceived advantages to playing the first (or last?) piece, so enough games should be played to allow each player a turn at starting.

The first player takes a pentacube from the 12 available and lays it on its face in the centre of the table. There is no score for this.

The second player takes a pentacube from those remaining and places it on its face so that one of its corners touches a corner of the first piece. Vertical faces of the touching corners should be at 90 degrees.  There is no score for this.

The next player takes a pentacube and places it using only one hand in any orientation, above the first two pieces so that at least one unit face on the piece touches at least one unit face on each of the first two pieces, and no part of the third piece is below the tops of the first two pieces.  The player scores one point for each face of his piece which touches a face of one of the first two pieces.

Play progresses with each player in turn adding a pentacube to the pile, using only one hand, in any unit face to face orientation. A player scores one point for each horizontal unit face of his piece which touches a horizontal unit face of one of the existing pieces, and two points for each vertical unit face of his piece which touches a vertical unit face of one of the existing pieces.  It is forbidden to play a piece in such a way that one of its upper faces touches the underside of a previously played piece, as this could destabilise the pentacube pile.

After all pieces have been played, points are totalled for each player.  New games take place until each player has taken a turn at starting.  The highest-scoring player wins.

We’ll now go through a game step by step, highlighting scoring and illegal moves.

Left, an invalid first move. The piece must lay flat.

Above, a piece is played on its face, near the centre of the playing area.

Above, a second piece is played, touching the first corner to corner, forming a 90 degree angle.

Above, an invalid second move. The V pentomino isn’t touching the first piece corner to corner.

Below, another invalid second move.  The V pentomino isn’t touching the first piece at 90 degrees.