As my gift for the holidays, can you solve this math problem without pencil, paper or calculator?

Is this a homework question??

One

To find the sum of the integers from 1 to 1,000,000, divide 1,000,000 by 2 and write the result down twice: 500,000,500,000. To find the remainder of a number after dividing by 9, add up the digits of the number until you get a single digit answer: 5 + 0 + 0 + 0 + 0 + 0 + 5 + 0 + 0 + 0 + 0 + 0 = 10; 1 + 0 = 1; therefore, the remainder will be 1.

I’m not sure how this is a legitimate question since you clearly know the answer.

The answer is one, as the two jellies found. This is no homework problem, just something that I thought of.

Here is how I got the answer. Start by adding the numbers 1 to 9, which can be written as (1+8) + (2+7) + (3+6) + (4+5) + 9. The important thing to realize is that this is divisible by 9.

Now consider the sum of the next 9 numbers, 10 to 18. After 9, the remainders when divided by 9 repeat themselves. 10 has a remainder of 1, 11 has a remainder of 2 and so on. Therefore the sum of the numbers from 10 to 18 has the same remainder as the sum from 1 to 9. and so is also divisible by 9.

We can apply the same argument to each successive group of 9. One million = 9×111,111 + 1. There will be 111,111 groups of 9, whose sum is divisible by 9, leaving just 1,000,000, whose remainder when divided by 9 is 1.

Why would I want to give you a gift?

Perhaps I should have phrased things differently. The problem is my gift to everyone else. Since I already know the problem and how to solve it, there isn’t anything in it for me.

I’m working on it… I got the sum pretty easy. ..., I’m having a little trouble with the division and carry…. 5.5 ..5
Ooooo. it changes in the middle…1 1 1 I’m sticking with 1
That was fun! Thanks for waking up a couple of brain cells.

Shoot me