Problems

# Readers' Problems

How many pairs of supplementary angles can be found in the diagram below? • Submitted by Lucas Motaung, Hartswater

Prove that the circumcircles of triangles OAB, OBC and OCA, where O is the orthocenter of triangle ABC, have the same radius.

• Submitted by Prof Poobhalan Pillay, University of Durban-Westville.

Prove that the fourth power of an even number which does not end in a zero, ends in a six.

• Submitted by Louis Brewis, De Kuilen High School In the figure, PQRS is a square and T is a point inside the square such that PT=5, QT=4 and RT=1. Find the area of the square.

• Submitted by Mundia Mubyana, Pretoria Boys' High School

A farmer had 14 cows and three perfectly logical sons. On his deathbed he divided the cows so that all had some, the eldest had more than the middle who had more than the youngest. He told each son secretly how many he was to get. Then in front of all he asked the eldest if he knew how many the others had. The answer was 'No'. Then he asked the middle son the same question. Again the answer was 'No'. Then he asked the youngest son, and yet again the answer was 'No'.

Starting again, the old man asked the eldest son if he knew how many cows each of them was to get, and again the answer was 'No'. But when he asked the middle son, the answer was 'Yes'.

How many cows did each of the sons get?

• Submitted by Biddy Greene of the Unversity of Cape Town