Shakuntala Devi was asked to find the 23rd root of a
201 digit number. She found the answer in 50
seconds. After a lengthy program was written and
13,000 instructions were fed into a computer the
machine gave the same answer, but it took a full
Shakuntala Devi refers to her calculating powers as her
gift". She lives in Calcutta and often travels, giving demonstrations
of the talents.
THE FIRST BY THE FIRST
AND THE LAST BY THE LAST
This formula provides us with two very simple and very quick checks on our calculations and another special type of multiplication. A third checking device is also shown in this chapter.
by multiplying the first figure of each number together we find that
since 600 × 80 = 48,000 and we know the answer will be more than this we can say the answer is about 50,000.
39 × 61 is approximately 2400
here we can think of 39 as (that is 40 - 1) so that the first by the
383 × 887 is approximately 300,000
400 × 900 = 360,000 and the answer must be below this because
Thus we see that The First by the First gives us the first figure of the answer; and the number of figures in the answer is also evident.
by multiplying the last figure of each number together we get the
since 3 × 7 = 21, which ends with a 1.
So if we are finding 33 × 8 by doubling 33 three times, and we arrive at 132 but we lose track of how many times we have doubled, we note that the last figure of 33 × 8 must be 4 and that 132 cannot therefore be the answer. But doubling once more to 264 we are now confident that we have the correct answer.
This is another checking device which can be very useful and which comes under the Vedic formula The Product of the Sum is the Sum of the Products.
Every number, no matter how long, can be reduced to a single figure, called its digit sum, by adding the digits in the number and then adding again if necessary.
So for 43 the digit sum is 7 since 4+3 = 7.
Also for 47: 47 = 11 = 2.
And 876 = 21 = 3.
To check a multiplication sum the above Vedic formula reads: The Product
of the Digit Sums is the Digit Sum of the Products. So if we have the
we reduce 74, 76 and 5624 to their digit sums: 74 = 11 = 2,
Then replacing the original sum with these digit sums we get
To check 88 + 77 = 165 for example, the sum becomes 7+5 = 3 in digit sums, which is correct.
This digit sum check does not detect certain errors however: if we wrote
88+77 = 156 the digit sum check would be the same as above even though the answer is wrong. However in this case The Last by the Last tells us that the answer certainly is wrong since it must end with 5.
This complements the last multiplication type in the previous chapter in which the first figures are the same and the last add up to 10.
The conditions are satisfied here as 2 + 8 = 10
So we multiply the first figure of each number together and add the
1. Can you find out how to extend the method to the following two cases?
a) multiplying numbers in which the first figures add up to 10
and the last two figures are the same: e.g. 212 × 812,
b) multiplying numbers in which the the first two figures add up to 100
and the last two figures are the same e.g. 987 × 027.
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