Volume 17


On several occasions I have been in the position of having to cook a roast dinner. My experience in this field is rather limited and so I have to rely on cookbooks to provide cooking temperature and time.

In the last issue, we posed the innocent question: "How long is the coast of Australia?" Some sceptical readers have queried our conclusions, which was, as you will recall, that the question is not as innocent as it seems.

In trying to deal with questions such as:

  1. In a new housing sub-division, how many letter boxes should Australia Post provide and where should they be placed?
  2. What is the most effective way to divide the fuel between the stages of a multistage rocket?

"Size of body is no mere accident. Man, respiring as he does, cannot be as small as an insect, nor vice versa... In fact each main group of animals has its mean and characteristic size..."

Let us pose the question: is it possible to form a rectangle (or even better, a square) by putting together smaller squares, all of which are different?

Andrew Jenkins, who devised the Cross-Numbers sent us not only the solution, but the detailed reasoning leading to it. We print it here in full.

Q.503 A rectangle 11cms $\times$ 7cms is divided by ruled lines into 1cm $\times$ 1cm squares, each containing a button.

Q.479 If $a679b$ is a five-digit number (in base 10) which is divisible by 72, determine $a$ and $b$.