| SOLUTIONS ('86/12) The winning solution to the prize puzzle in the September 1986 issue of Computing with the Amstred was sent in by Geoffrey Franklin of Alvechurch, Birmingham. He solved it using graph paper, producing the diagram shown in Figure III - the micro was only used to check that the result worked with the published program. Geoffrey's prize is a copy of Grasp, a graphical package to display and help solve equations.
Solving the dropping bricks problem in the November 1986 issue of Computing with the Amstrad believe it or not is ALL that sequential computers do. It is called a Turing machine after the British mathematician Alan Mathieson Turing who invented it in the 1930s. It was a pure "thought" machine and yet it revealed certain fundamental limitations on what any computer (or human) can calculate. Certain problems, although they must have an answer, are non-computable. Probably the most famous of these problems is to decide whether or not a given Turing machine (or program) will stop. A subset of this problem is to find, for a given number of cards, the stopping program that leaves the most bricks in the rooms. This is called the Busy Beaver problem and, although studied for
more than 20 years, the answer for five or more cards is still unknown. In order to explain and clarify the problem, I have written Program II which accepts any five card set of instructions. The rooms are in the array R with P as the pointer to the current room. Note that there are a generous 700 rooms and P starts in room 20. Line 110 does all the work. From the data it gets the next three instructions which tell it to: (1) Drop a brick or dear the room f5 or 0 in R(P)). (2) Move East or West fadd 1 or-1 to P). (3) Get the next three data items and count moves until ON ERROR. If you run this program you should find that it takes about 23 minutes to make 134,467 moves, which leave 501 "bricks" or 5s in the array R. | 
