# Sum Of Digits Are Just Fun

Suddenly I noticed a common property of any number while solving a problem like what is the sum of digits of the product of 61s 3 that means 33333.........3333 and 62s 6 means 666......6666.For 3 and 6, as 6 is twice of 3, the sum of digits of their product follow a specific rule.

After solving the problem , i thought that , Does every number contains this property ? So I tried to find the sequence for 2 and 4 also. As 4 and 8 are twice of 2 and 4 , so i considered the products of any certain number of 2 suppose n , and n+1 numbers of 4. Then i took product of the numbers and then calculated the sum of digits of the number combined with 2 and 4 like 22444 and then calculate the sum of digits of the product of two numbers 22 and 444 . Then i calculated Sum Of Digits(Products)- Sum Of Digits(Numbers) . And i saw that the result follow a rule . Just see the image bellow to understand what I've done :

Please notice the series carefully. If you subtract 1st term from 2nd term then you'll get 8. By the same process the difference of every 2 term till 10th term are 8, 6, 4, 2, 0, -2,- 4, 12 and 1. Then this repeats again and again till infinity. So , It's clear that there is a strong logic behind this sequence.

Now for the number 4, I did same process again . And at first see the image :

Now notice that after 20th term the Sum Of Digits(Numbers) - Sum Of Digits(Products) follows a sequence. it is : -7 -7 -7 -7 2 -7 -7 -7 -7 2 -7 -7 -7 -7 2 -7 -7 -7 -7 2 And the mod of Sum Of Digits(Numbers)% Sum Of Digits(Products) follow a specific rule after 20th term : 64 66 68 70 2 65 67 69 71 2 66 68 70 72 2 67 69 71 73 2

You can try it for any other numbers too. Thanks for reading this. You can download my Microsoft Excel files from my website MathMad.

Note by Arindam Kumar Paul
5 years, 1 month ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

Can you explain why this pattern exists?

What is the math behind it? How would we find the sum of digits of this product?

Staff - 5 years, 1 month ago

I don't know why this types of pattern exists ? But i found different logic for different numbers. If you know , please explain in details. I want to know more about this. But i believe that patterns and numbers are everywhere. I worked for a thesis paper last year and their i also found a pattern . I don't know about any specific reason behind it.

- 5 years, 1 month ago

If a hemispherical bowl is 4 cm long. It is filled upto 3 cm. What volume of bowl is filled?

- 5 years, 1 month ago