Question

The number 55 is multiplied by a 55 digit number that contains only ones. What is the sum of the digits of the product

Answer 1

Answer:

$Sum = 64$

Step-by-step explanation:

Given

$n = 55$

$x \to 55\ digit$ 1's

Required

The sum of the $digits$ of the $product$

To do this, we start with smaller numbers

$55*11 = 605$  ---- 2 digits

$55*111 = 6105$ --- 3 digits

$55*1111 = 61105$ -- 4 digits

$55*11111 = 611105$ -- 5 digits

$55*111111 = 6111105$ --- 6 digits

Notice that as the 1's increase on the left-hand side, the 1's increase on the right-hand side

The difference between the count of both 1's is 2 1's

So, for n digits, we have: 6[n - 2, 1's]05

So, the sum is:

$Sum = 6 + (n - 2) + 0 + 5$

For 55 digit, $n = 55$

So, we have:

$Sum = 6 + (55 - 2) + 0 + 5$

$Sum = 6 + 53 + 0 + 5$

$Sum = 64$