Calculators Won't Work! 1

Algebra Level 3

Find the sum of digits of the product below.

123456789 × 999999999 \large 123456789 \times 999999999


The answer is 81.

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1 solution

Nathan Laurence
Nov 23, 2016

Try the following multiplications:

99 99 * any number, the sum of the digits is 18

999 999 * any number, the sum of the digits is 27

9999 9999 * any number, the sum of the digits is 36

Now if you look carefully, there is a pattern which is look at how many 9s are there multiplied by 9 ;

Similarly, 999999999 999999999 * any number, the sum of the digits is 9 9 = 81 9 * 9 = 81 .

Hence, the sum of digits of p p is 81

99 101=9999 sum is 36 so just change the solution appropriately before generalizing: 99 any 1 or 2 digit number , sum of digits is 18.

Ajinkya Shivashankar - 4 years, 6 months ago

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Good point! Generalizations without proof is quite unacceptable. However, noticing this pattern is very elegant.

William Nathanael Supriadi - 4 years, 6 months ago

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