The sum of n natural numbers is three digits number and all digits are the same. The same digits is 6 and the sum is 666.
A three-digit number with the same digits is the sum of n natural numbers.
Let's say the sum of n natural numbers is bbb.
Then,
n( n + 1) / 2 = bbb
n( n + 1) / 2 = b( 111 )
n( n + 1) / 2 = b ( 3 × 37 )
n( n + 1) = 6b × 37
Now, the left-hand side of the equation is the product of two consecutive natural numbers.
Therefore, the right-hand side of the equation is also the product of two consecutive natural numbers.
Hence, 6b = 36
b = 36/ 6
b = 6 and n = 36
As a result, 36 numbers have been added together, and their total is 666.
Learn more about natural numbers here:
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