Saturday, October 21, 2000
M I N D  G A M E S


Kindergarten rivalry

EINSTEIN and Newton join the kindergarten on the same day and straightaway recognise a potential rival in each other. They are polite to each other, but are always thirsting for an argument.

Einstein gets a chance to prove himself soon when he and Newton are left alone in the classroom for some time. He writes an eight-digit number on a paper and shows it to little Newton. The number is 12345679.

"Take this pencil and circle one of the digits," he tells Newton. Newton promptly circles seven. "Multiply the eight-digit figure by 63 and see what happens," Einstein says. Newton obeys and is amazed to find that the answer is a row of sevens.

1 2 3 4 5 6 7 9

x 6 3

7 7 7 7 7 7 7 7 7

"I must admit that I am amazed," Newton says. Einstein replies, "When you circled one of the digits, I mentally multiplied that number by nine and asked you to multiply the eight-digit figure by that number. When the number is multiplied by 63, it always produces a row of sevens. If you had circled the number two, I would have asked you to multiply the eight-digit number by 18 (i.e. 9x2) and it would have given us a row of twos."

Some years later, when the two odd boys are in a higher grade, Newton decides to get even with Einstein. "Choose a number, but do not reveal it to me," says Newton. Einstein obeys. "Add 5 to it and double the result. After that, subtract 4 from it. Divide the result by 2. Now, subtract the number you had thought from the result you have obtained," Einstein follows all the instructions. "The result is 3," declares Newton and Einstein can only agree.

"Even if you had picked a different starting number, the result would always have been 3. This thing called algebra which is being taught to us is amazing. The teacher says that you and I have an exceptional talent and as we progress through our mathematical career we will learn to use algebra more," Newton says.

 

"I think we should not accept a proof simply because it works for a bunch of random numbers," Einstein says. Newton says, "You can devise your own tricks by using algebraic equations where the secret number is always x. I had assumed the number that you had thought earlier as x. Add five to it to get x+5. Double the result to get 2(x+5) or 2x+10. Subtract 4 to get 2x+6. Divide by 2 to get x+3. Now, subtract the original number (x) to get 3. I memorised an equation and made your thoughts deviate from the origingal number. You can use any variable you want to start with, but you must always finish with a number."

The boys grow up and join the biology course in the college, but remain mathematicians to the core. By now, both have become rather absent-minded and confirmed geniuses. The biology teacher tells them that amoebas are one-celled animals that reproduce by dividing in two. One amoeba becomes two, two become four, and so on. If these organisms get enough food, they can double their population every 24 hours.

The teacher says, "If you begin with just one amoeba in a jar of pond water at 10 am on Monday, imagine how many amoebas will be in the jar by Wednesday of the next week at 10 am!"

"512," The boys yell out together.

"512 what?" says the teacher. Newton says, "512 amoebas Sir. Exactly nine days pass between 10 am on Monday and 10 am the following Wednesday, so the amoebas have a chance to double their population nine times."

Monday: 1 amoeba

Tuesday: 1x2=2 amoebas

Wednesday: 2x2=4 amoebas

Thursday: 4x2=8 amoebas

Friday: 8x2=16 amoebas

Saturday: 16x2=32 amoebas

Sunday: 32x2=64 amoebas

Monday: 64x2=128 amoebas

Tuesday: 128x2=256 amoebas

Wednesday: 256x2=512 amoebas

"This is too tedious. Another way to calculate this is to use exponents. 29=512.

Years pass. The two mathematicians are now well past their prime and are in a mental asylum. Mathematicians never get old, they only lose some of their functions. Almost all of them become mad and so have these two, but the rivalry is still fresh.

Newton says, "I have a theoem which says that a cat has nine tails. The proof is that no cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails."

Einstein says that he can prove anything if given that 1+1=1. Newton asks him to prove that he is the Pope on the basis of this. Einstein says, "I am one. The Pope is one. Therefore, the pope and I are one."

Aditya Rishi