The Tribune - Windows

Newton’s birthday

IT is Newton’s fifth birthday and he has invited seven of his best friends to the party, for whom he has prepared a delicious chocolate cake. The friends arrive at the right time and everything seems fine, but Newton does not know that they have mischief on their mind.

"It is a splendid cake that you have baked Newton, we hope that it tastes just as good," the boys say. "I have worked hard on it friends, everything is in correct ratio and proportion. I am sure that all of you will like it," Newton says. The birthday boy prepares to cut the cake, but before he can even graze it with the knife, the friends stop him again.

"Newton, do you love all of us equally?" they say. "Of course, I do, but why do you ask that?" says Newton. "We say so because we want you to divide the cake into eight equal pieces," they say. "If that is what you want, I will not only divide the cake into eight equal pieces, but also do it in three cuts," says Newton.

"What is so difficult about that?" says a friend. "Why don’t you try it for yourself?" Newton throws him a challenge. "With your birthday cake?" is the friend’s shocked reply. "I have some other cakes that do not have toppings," Newton assures him. "Alright," says the friend.

One of the spare cakes is brought to the table and one of the friends prepares to cut it as Newton and the others observe. The friend makes three cross cuts that meet in the centre of the circular cake and counts the divisions — six.

He ponders over the problem for some time before giving up and making way for the second boy to try. The second boy assumes his position before the cake and thinks a lot before making a move. He makes two cross cuts that meet in the centre of the cake and the third cut is across the face of the cake, cutting each of the two lines at a point. However, this divides the cake only in seven unequal pieces.

The friends realise that the problem is much more complex than they had imagined and wonder how Newton would solve it. They turn to the child mathematician as he prepares to cut his birthday cake. Newton makes two cross cuts that divide the cake into four equal parts. The third cut that he makes is horizontal, halfway down the height of the cake, cutting the cake in eight equal parts. The friends are so amazed that they forget to collect their share of the cake.

"Newton, we are impressed, you are a wizard. Show us more tricks," say the friends. "Fine, I’ll show you something else that I have discovered. How many of us know the tables?" says Newton. Only two hands come up. "Boys, do you know the table of 9?" Newton says. "We find it hard to remember," say these two. "You don’t have to remember it because the table is on your hands," says Newton. "How is that?" the friends want to know.

Newton says, "Spread your hands. Beginning from the thumb of your left hand, number your fingers from 1 to 10. If you want to multiply 9 by 5, fold finger number five, which is the little finger of your left hand, and count the number of fingers to the right and left of it. You will find four fingers (including the thumb) to the left of it and five to the right of it.

The number of fingers on the left (4) gives you the first digit and number of fingers on right (5) gives you the second digit. So, 9x5=45. Simply fold the finger of the number that you wish to multiply with 9 and get the answer straightway by comparing the number of fingers to the right and left of it.

Table of 9 on your hands

Beginning from the thumb, fingers are numbered 1 to 10. If you want to solve 9x2, fold finger 2. Count the fingers on the left of this (1) to get the first digit. Count the fingers on the right (8) to get the second digit. So, 9x2=18

In case of 9x10, there are 9 fingers to the left of the tenth and the folded finger and zero to the right of it. So 9x10=90."

"Newton, you take the cake," say his friends.

— Aditya Rishi