By J M Ovelil
Melchi was overwhelmed with joy when he got the news that he was selected to go to St Thomas College, California. It was a student exchange programme and Melchi was doing his final year graduation in mathematics in St Bartholomew College, Margao.
Though the exchange program was only for a month, the student was expected to make the necessary arrangements for boarding, lodging and meet the expenses for the same. As soon as he reached California, Melchi met the principal of St Thomas College, who gave a few addresses of people who were willing to keep paying guests. He decided to stay with an old childless couple of Indian origin, hoping that the expenses for boarding and lodging would be affordable to him. He learnt from other students that the normal weekly expenses would be between 50 to 60 dollars.
The landlady Ms Ruparel appeared very friendly and was very happy to keep young Melchi as her paying guest. “Madam, how much should I pay for a week for both boarding and lodging?” Melchi asked her.
The old lady began to explain, “You have to make the payment only at the end of every week and the amount would be calculated on the basis of the expenditure for the week. Don’t worry; I shall let you know the amount at the end of every week.”
So Melchi was happy and a week passed quite fast. At the end of the first week Ms Ruparel informed the young scholar, “Yes, Melchi, the daily expenditure for this week is only $ 9. So you can pay me 63 dollars for the week”. The youngster was very happy and paid the amount immediately.
At the end of the second week Ms Ruparel told the guest, “The daily expense for this week is gone up a bit and it comes to $12. So pay me 84 Dollars for this week.”
Though the paying guest was not very happy, he promptly paid the amount and the madam was delighted. Another week passed and the young guest anxiously waited to know the amount he has to pay. The host told the young mathematician, “Melchi, I am very sorry. The costs of things are going high and your daily expenditure comes to 15 dollars. So kindly pay me 105 dollars for this week.”
The young Indian realised that the old lady was greedy and she was cheating him. He was annoyed. The quality of the food remained the same but the amount was steadily increasing. The youngster realised his mistake of staying with the Indian couple. However he paid the amount.
Finally it was the end of the fourth week and the arithmetic progression continued. The greedy host announced the expenditure - 18 dollars per day. The Indian student was very upset and angry. He knew that the lady was out for money and she was a cheat. So he made up his mind to teach her a lesson. The mathematician knew that the old lady was weak in arithmetic and she was fully dependent on a calculator for all calculations. So the young mathematician decided to play some mischief with arithmetic - some arithmetical tricks. “How much am I to pay for the week?” he asked her gently. Soon her fingers moved on the calculator. “18 x 7 = 126 dollars only,” replied the lady.
“18 x 7 is not 126, madam. It is 63,” Melchi told her very clearly.
“What did you say? 18 X 7 is 63?” she laughed at him. “Do the multiplication and show me,” the old lady, challenged Melchi.
Melchi wrote on a piece of paper, 18 and below 7 and said, “7 times 8 = 56,” and wrote it down. Then he said, “7 times 1 = 7” and wrote it below 6. Finally he added. .56+7= 63. (as shown below)
The lady was puzzled. “No, no, look at this calculator,” she murmured.
“Your calculator is wrong. I am a mathematician,” was his firm reply.
“O.K. Very good! Please, divide 63 by 7 and if you get 18, I will agree with you,” the clever lady outwitted the mathematician.
Melchi smiled and wrote 63 immediately. He wrote 7 on its left side (divisor) and also 1 on the right side (quotient). He then asked “What is 7 times 1?”
“7”, the lady answered.
Melchi wrote down 7 below 3 and asked again, “What is 13 – 7?”
“6” she said and the guest wrote it below. He brought down 5 so the number was 56. Then he wrote 8 next to 1 and said 7 times 8 = 56. He subtracted 56 from 56 and wrote 0 and hence 63/7 = 18. (As shown below)
The lady was frantic but was not prepared to give up. She shouted in anger, “Don’t try to fool me. Write 18 one below the other 7 times and add. If you get 63 you don’t pay me anything.” The old lady had trapped the young mathematician. The mathematician smiled and told the greedy American lady, “O.K, madam. No problem. Done,” and wrote exactly the way she had asked and began to very slowly add all the 8s one by one 8 + 8 = 16, 16 +8 = 24, 24 + 8 = 32, 32 + 8 = 40, 40 + 8 = 48, 48 + 8 = 56. Once he got 56, he, added all the ones to 56 as quick as he could, 57,58,59,60,61,62,63 and wrote it down. The sum was 63 and he proved it. (See below)
Ms Ruparel was confused and. humiliated. “Why are you doing this to me?” The host asked in frustration. “Why are you doing this to me?” the guest retaliated with a smile. “I know very well that the actual expenditure for a day will be less than 10 dollars. But 10 is quite reasonable. You increased it from 9 to 12, then to15 and now to 18. Why are you so greedy? You are a rich lady with no children.” Hearing that, the host burst into tears and apologised. “Please don’t get angry with me. Pay whatever you like,” she pleaded. Melchi too felt sorry for the old lady. He too apologised for fooling her with numbers and soon they became good friends.
