#1**+1 **

What the SUM of the digits of this number? 1,000,000,001 =2. Is 2 divisible by 2? Next number:1,000,000,003 =4. Is 4 divisible by 2? Next number: 1,000,000,005 =6. Is 6 divisible by 2?....etc.

What are you looking for? Can you give an example, say of a much smaller number, explaining exactly what you want?

Guest Aug 25, 2020

#6**+1 **

But that is exactly the reason it begins with 1,000,000,001. This number is NOT divisible by 2!!. Only the SUM of its digits, which is; 1 + 1 = 2 is divisible by 2. Do you actually understand the answer that was given to you? Similarly, the last number: 9,999,999,999 is NOT divisible by 2, but the SUM of its digits which equals 90 is divisible by 2.

Do you see it?

Guest Aug 25, 2020

#7**+1 **

OK young person! Here is a computer code that I wrote in Python 3 to count ALL 10-digit numbers whose SUM is divisible by 2!!

%%time

# Efficient Python 3 program to sum up the #

# multiples of digit n in a range of 2 - 10-digit integers #

# E.G. "What is the total number and sum of all 3-digit integers that are

# mutiples of 7, or are divisible by 7?". Answer =70,336 #

# find the Sum of having n digit

# and divisible by the number

def totalSumDivisibleByNum(digit, number):

# compute the first and last term

firstnum = pow(10, digit - 1)

lastnum = pow(10, digit)

# first number which is divisible

# by given number

firstnum = (firstnum - firstnum % number)+number

# last number which is divisible

# by given number

lastnum = (lastnum - lastnum % number )

# total divisible number

count =int ((lastnum - firstnum) / number+1 )

print("Total count =", f"{count:,d}")

# return the total sum

return int(((lastnum + firstnum) * count) / 2)

# Driver code

digit =10 ; num = 2

print("Total Sum =", f"{totalSumDivisibleByNum(digit, num):,d}")

**Total count = 4,500,000,000 Total Sum = 24,750,000,004,500,000,000**

Wall time: 0 ns

Guest Aug 25, 2020