Lateral Thinking (Assumption Breaking)

These solution notes challenge assumptions about sequence, rows, and stacking. The original problem statements and diagrams are not supplied, so the notes do not fully specify the required arrangements:

Solutions

1. One way is shown on p. 89. This is a ‘circular’ arrangement in which each block has two touching neighbours — one in front and one behind.

2. There is often some difficulty because it is assumed that the problem has to be solved in the sequence in which it was posed (i.e., one block to touch one other, one block to touch two others, one block to touch three others). If a start is made at the other end by making one block touch three others, then this arrangement can be progressively modified to give the arrangement shown.

3. Some people have a lot of difficulty because they assume that all the blocks have to lie in the same plane. As soon as one breaks free of this assumption and starts to place the blocks on top of one another, one can reach the required arrangement.

4. There is a surprising amount of difficulty. The usual mistake is to arrange the blocks in a long row. In such a row the end blocks touch only one other, but the middle blocks have two neighbours. The correct arrangement is very simple.