Problem 5
The digital root of a
number is obtained by adding the digits of the number until a single digit is
obtained. The digital root of 943561 is
1 because 9 + 4 + 3 + 5 + 6 + 1 = 28, 2 + 8 =10, 1 + 0 =1. A number is called a
triangular number, if it is equal to
the sum of the first n natural numbers. Find all digital roots of triangular
numbers that are not triangular numbers themselves.
[Problem submitted by Iris Magee, LACC
Associate Professor of Mathematics.]
Solution for Problem 5:
The only such digital
root is 9. Observe in the following
chart that the “digitalroot pattern” repeats.
The only digital roots of triangular numbers are 1, 3, 6, and 9. The first 3 are triangular numbers
themselves.
Triangular Numbers

Digital Roots

1 
1 
3 
3 
6 
6 
10 
1 
15 
6 
21 
3 
28 
1 
36 
9 
45 
9 
55 
1 
66 
3 
78 
6 
91 
1 
105 
6 
120 
3 
136 
1 
153 
9 
171 
9 