Painless Nine Times (II)

Although, most of you would have successfully found out answers for the nine times twenty-five or nine times thirty-four on your fingers, let us revise some more facts for better understanding of the procedure involved.

In the last article we saw how to remember nine times one to nine times ten on our fingers. Let us now try to extend the same idea to remember nine times eleven to nine times twenty on our fingers. In order to get the clue for working out more nine times on fingers let us first write down nine times of eleven to twenty, as shown below.

Let us observe the products in the table reproduced here. The very first thing we observe is the appearance of 'one' in the hundreds place of all the products except the first, which is nine times eleven. It means we will have to reserve one finger permanently for representing one of the hundreds place.

Next, we add the individual digits of all the products and observe the sum. What does it reveal? Except for the first product, which is nine times eleven, digits of all the products add to nine! Another observation, which is parallel to the earlier one is, the last two digits (i.e. the one in the tens place and the one in the units place) always add to eight.

These observations tell us that with the help of the nine fingers, after reserving one for hundreds, we can manage to show the last two digits of all the products, of course except that of the nine times eleven.

As an example, two products are shown in the figure here. Take a look at the example (a), first. For showing nine times twelve, we bend the second finger of our left hand. Why second finger? For representing the two in the number twelve! Now, the finger indexed one will always represent one hundred. Besides that one, there is no other finger to the left of the bent finger. It means there is zero in the tens place. Since, there are eight fingers to the right of the bent finger, in the units place we will have eight. Thus, nine times twelve will be one-zero-eight or one hundred and eight.

Similarly, in the example (b), for remembering nine times eighteen, we bend eighth finger, which is on the right hand. Having reserved the first one for one hundred, we count the remaining fingers to the left of the bent finger. These are six; therefore we will have six tens. To the right of the bent finger we have two fingers. Thus, there are two in the units place. In short, nine times eighteen is one-six-two or one hundred sixty-two.

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