# Little tours in mathland

S N Gananath

A little girl was deeply engaged in something. She counted on her finger tips repeatedly but something was amiss, the girl became restless, her frustration was evident. Her father who had just returned from work wanted to help her. “What happened, darling?”, he asked. The girl explained that she was counting numbers in an unusual fashion like this.

All she wanted to find out was the finger she would touch on reaching the number 10000. This she was doing by brute force and was obviously failing. Her father was a mathematician who taught at a university. He figured out the answer in no time and gave it to her. The girl could not believe it! “How did you find out?” she asked. “Look, I am a mathematician and so it is easy for me,” he said. As the story goes, the daughter was so fascinated by the power of mathematics that she pursued the subject and became a mathematician herself.

A major misconception among mathematics teachers and children relates to the idea of mathematical investigations. They seem to believe that such investigations can be pursued only by trained professional mathematicians and not by schoolchildren. This is incorrect and rather unfortunate. Most children can perform such investigations although their ‘results’ are not necessarily original. They may not be ‘publishable’ but can be deep and profound as far as the child is concerned. Here are some indicative paths of discovery that children can try and enjoy.

1. The temple problem
A mathematically interesting folk problem, popular in different parts of India goes something like this.

A village has three temples and a pond in front of each. A devotee goes with a certain number of flowers in his hand. He immerses the flowers in the pond before he enters temple #1. The pond has divine powers and the number of flowers get doubled, i.e., if he carried 5 flowers, it becomes 10, 6 becomes 12 and so on. He uses a certain number of flowers to worship the deity in temple #1. Then with the remaining he goes to the pond in front of temple #2. The flowers get doubled again. He worships with exactly the same number of flowers as in the first temple and some flowers remain with him after temple #2. Then he goes to pond # 3 and they get doubled. He worships with exactly the same number of flowers in temple #3 and his hands are empty now.

The author was a mathematics teacher at Rishi Valley School and is currently the Director of Suvidya Educational Centre, Mysore. He can be reached at sngananath@gmail.com.