The puzzles on the table
 Cut and fold a 3 X 5 card to make this. Can you place 31 dominoes on the 62 squares?  (Two of the chessboard squares are gone.) Pack the blocks (18) in the box. Pack the blocks (6) in the box. Arrange the ellipses so that the closer they are, the more similar--and the more similar, the closer. This one is spatial visualization, not abstract math.  The insights into the mathematical abstractions generally develop at the beginning of adolescence.  Children may see it when their parents don't. Counting squares to discover that 62 = 62 is only a beginning here.  Noticing that a parity relationship exists is a very small step, but it's a step toward the more abstract...seldom seen.  It is, however, very easy to see. This puzzle is virtually unsolvable by trial and error.  The arithmetical principle of the smaller puzzle (to the right) is a virtual necessity for this puzzle. Construction instructions below. This puzzle yields easily to trial and error.  It can, however, be solved by a simple arithmetical principle. ...and it's the same principle that solves the 5X5X5 cube puzzle to the left This puzzle has, in our opinion, as great a potential toward more effective understanding of the role of mathematics and science in human life as can be found.  Click on the picture to see how our concept of measure has been expanded in ways seldom seen.

 These blocks can be packed into a larger cubical box with no spaces unoccupied and nothing sticking out.  This looks very easy.  It is not!  Both this puzzle and the smaller puzzle of putting six blocks into a 3 x 3 x 3 box can be reasoned; it's not just a matter of trial and error.

The majority of the blocks are those brick shaped ones.  There are thirteen of them, each one unit by two units by four units.  There are three blocks one by one by three units.  There is one block one by two by two units, and one block two by two by two units.
 no. dimensions vol. 13 1 X 2 X 4 104 3 1 X 1 X 3 9 1 1 X 2 X 2 4 1 2 X 2 X 2 8 18 <—totals—> 125