Digital Root

Number Theory Level 2

The repeated digital sum, or digital root of 6788 is 2.

6+7+8+8 = 29

2+9 = 11

1+1 = 2.

What is the Digital root of the 180 digit number 1011121314.... ....96979899 made from the numbers 10 to 99 ?

9 4 1 7

Satyen Nabar by Satyen Nabar , 48, India

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2 solutions

Satyen Nabar
Jun 16, 2014

If the digits are grouped as 1099, 1198, 1297, ..... etc we get 45 digit sums of 19 each. 45 x 19= 855. 8+5+5 = 18. 1+8 = 9.

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Rishabh Jain
Jun 17, 2014

a simple and elegant solution 10 + 11 + 12 + . . . . + 99 = 90 2 ( 10 + 99 ) = 45 × 109 = 9 × 1 = 9 10+11+12+....+99=\frac { 90 }{ 2 } (10+99)=45\times 109=9\times 1=\boxed{9}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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