10 or 100

Number Theory Level 2

What is the sum of all digits of 10 20 − 2 \color{#D61F06}{10}^{\color{#3D99F6}{20}}-\color{#624F41}2 ?


The answer is 179.

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Sudoku Subbu by sudoku subbu , 19, India

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3 solutions

Akash Gupta
Jan 30, 2015

10^20-2 this means
10000...(20 times 0)
subtract 1 means 20 times 9
subtract 2 means 19 times 9 and then 8
i.e, 19X9+8
171+8
179


4 Helpful 0 Interesting 0 Brilliant 0 Confused

When you subract 1 from 10^20 you would have have a total of 19 digits. Out of those 19, 18 are the digit 9 and one is 8. So the total should be 18*9+8=170

Drishya Premchandani - 5 years, 5 months ago
Sudoku Subbu
Jan 28, 2015

1 0 20 − 2 = 99.............98 [ 19 t i m e s ] 10^{20}-2=99.............98[19times] => sum of all digits = ( 19 × 9 ) + 8 (19\times9)+8 =171+8=179

2 Helpful 0 Interesting 0 Brilliant 0 Confused

10^20 has 21 digits out of which 20 are 0s and one 1. So subtracting 2 from it yeilds a 20 digit no. of which there are nineteen 9s and one 8. Sum = 19*9 + 8 = 179

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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