Cuisenaire tower

Wet dinnertimes always finished before we could finish building our Cuisenaire towers, so we never got to find out how tall the complete tower would be. The towers were built by laying two parallel rods E-W, then two more across them N-S, and so on upwards, starting with the longest rods.

Using the rod quantities from the modern 'International' set (sadly the rods, 35 years on, are now plastic rather than wood)

 Rod colour Rod length (cm) Rods Layers Total height reached (cm)
     Orange              10   10      5                         5
       Blue               9   12      6                        11
      Brown               8   12      6                        17
      Black               7   14      7                        24
   Dk green               6   16      8                        32
     Yellow               5   20     10                        42
     Purple               4   28     14                        56
   Lt green               3   36     18                        74
        Red               2   50     25                        99
      White               1  106     53                         *

In practice it would have been impossible to make many stable layers with the shorter rods (4cm downwards) so the maximum practical height would have been about 50cm.

The theoretical maximum using the 2-per-layer system would have been 99cm; one 1cm block on top would have reached the 100cm level, and I suppose under laboratory conditions the other 105 1cm blocks could have been stacked on top to reach 205cm.