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.