It has become customary for my daughter (6 years) to play with soapnuts everytime we visit my friend's place in Adyar. That evening, as we were getting ready to leave my friend's place, my daughter was busy decorating their stairs and said that she needed some more time to finish the decorations. I got curious about what she was doing. She showed me her idea behind the decoration -- one soapnut on the first step, two on the second step and so on till the tenth step. She was quite pleased with herself when she got to the tenth step and was ready to leave.
On the way back, during our bus ride, I was still pondering over the soapnuts decorations. I didn't quite know, until a day later, what was fascinating me about it. The next day I woke up with the formula (n * (n+1))/2 in my head. I must have remembered from my school days (thanks to all the memory work!) that this formula is used to sum a series of 'n' consecutive numbers ranging from 1 thru 'n'. But I didn't know how to arrive at this solution. At school, I was good at remembering stuff that was needed to score well. I didn't understand any concept deeply, neither did I need to!
For the first time in my life I really wanted to solve a math problem. The urge was so strong that I couldn't sleep that night. I was getting increasingly frustrated about my inability to solve this seemingly simple math problem. The next morning I was still at the problem while half-interestedly working in the kitchen. Later in the afternoon, we were preparing a garden bed. That's when it occurred to me that each pair of numbers (1,10), (2, 9), (3, 8), (4, 7) etc. in this series added up to 11 !! The rest followed fairly effortlessly. This gave me tremendous satisfaction, which I had never experienced before at school -- even when I scored 100% in Mathematics exams.
I was enthusiastic to share this experience with my children and started out with a picture of stairs with 10 steps and decorated it just the way my daughter had done before. I asked them to see how many soapnuts were used in that decoration. Later I asked them to imagine a staircase with 100 steps and asked them to see if they can figure out how many would be needed in this case. They both got interested in the problem and I left it at that.
- Hema
