# Sunday Times Teaser 2616 – Elevenses

### by H. Bradley and C. Higgins

#### Published: 11 November 2012 (link)

On 11/11 it is perhaps appropriate to recall the following story. In the graphics class students were illustrating pairs of similar triangles. In Pat’s larger triangle the sides were all even whole numbers divisible by 11. In fact they were 22 times the corresponding sides of his smaller triangle. As well as this, in the smaller triangle the digits used overall in the lengths of the three sides were all different and did not include a zero. Miraculously, exactly the same was true of the larger triangle.

What were the sides of Pat’s smaller triangle?

1. Here is my version:

2. I found the same result using an Excel sheet.
Should there be a control in your version to check that
whether the sides (a,b, c) will form a triangle or not?

• HI Naim,

There is a check to ensure that the sides form a triangle since, when a < b < c, the conditions for a triangle are b – a < c < b + a. And b – a < c since b – a < b < c and c < a + b because this is set as the loop termination condition on line 08