The number 55 was multiplied by a 55-digit number containing only ones. What is the sum of the digits of the result?
check with smaller numbers
55*11 = 605
55*111 = 6105
55*1111 = 61105
55*11111 = 611105
See a pattern? 6+(55-2)+0+5 = 64
To find the result of multiplying 55 by a 55-digit number containing only ones, we need to determine the number of ones in the result.
When multiplying a number by 1, the result is the number itself. Therefore, any number multiplied by a 55-digit number consisting only of ones will result in a number with the same number of digits, and each digit will be equal to 1.
The sum of the digits in a number consisting only of ones is the number of digits itself. Since the 55-digit number contains only ones, the sum of its digits is 55.
Therefore, the sum of the digits of the result of multiplying 55 by a 55-digit number containing only ones is also 55.
To find the sum of the digits of the result, we can break it down into a series of steps:
Step 1: Multiply 55 by a 55-digit number containing only ones.
To find the product, you can simply add the number 55 to itself repeatedly 55 times. Since the other number is a 55-digit number containing only ones, each term in the sum will be 55.
Step 2: Add the numbers together.
The sum of 55 added to itself 55 times can be calculated using the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term)
In this case, the first term is 55, the last term is also 55, and n is the number of terms (which is 55).
Plugging these values into the formula:
Sum = (55/2) * (55 + 55)
= (27.5) * (110)
= 3025
So, the sum of the digits of the result is 3025.