IBM Ponder This #167 · March 2012

Arrange the numbers 1, 2, 3,..., 63 on the nodes of a balanced binary tree of height 6 such that each distance 1, 2, 3,..., 62 is realized on an edge; i.e., it is the difference of two vertices which are connected with an edge.

Please supply the answer as a list of 63 numbers from top to bottom, left to right.

For example, here is a solution of the same problem for a tree of height 3 realizing all distances of 1, 2 ,.., 6:

Provide your answers in regular text format. The above solution, for example, in regular text format would be 7, 1, 3, 6, 4, 5, 2.

Solution

Best opened after a real attempt

To be added.