Question

6 row single digits sums ​

Answer 1

Answer:It is well known that the digits of multiples of nine sum to nine; i.e., 9→9, 18→1+8=9, 27→2+7=9, . . ., 99→9+9=18→1+8=9, 108→1+0+8=9, etc. Less well known is that the sum of digits of multiples of other numbers have simple patterns although not so simple as the case of nine. These are shown below:

Number Repeating Cycle

of Sum of Digits

of Multiples

2 {2,4,6,8,1,3,5,7,9}

3 {3,6,9,3,6,9,3,6,9}

4 {4,8,3,7,2,6,1,5,9}

5 {5,1,6,2,7,3,8,4,9}

6 {6,3,9,6,3,9,6,3,9}

7 {7,5,3,1,8,6,4,2,9}

8 {8,7,6,5,4,3,2,1,9}

9 {9,9,9,9,9,9,9,9,9}

10 {1,2,3,4,5,6,7,8,9}

11 {2,4,6,8,1,3,5,7,9}

12 {3,6,9,3,6,9,3,6,9}

13 {4,8,3,7,2,6,1,5,9}

It is asserted that the sum of digits follows a repeating sequence of length 9. This is so because for any decimal representation x, the number 10*x (ten times x) will have the same sum of digits. Multiplication by the base number 10 simply moves the digits one place to the left and puts a zero in the units place.

Step-by-step explanation:

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