Interesting property with 9

I want to get clarified with numbers ending with 9. I have considered 2 digit numbers and not extending it further as of now.

If we have 2 digit numbers of the form 10a + b and ending with 9,

Then, ab+a+b=10a+bab + a+b= 10a+b .

Note by Ashwin K
3 years, 8 months ago

No vote yet
1 vote

  Easy Math Editor

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.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. 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 1

paragraph 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 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

I assume that aa is a single digit positive integer and bb is a non-negative single digit integer, then obviously b=9b=9 and so your equation holds true.

Pi Han Goh - 3 years, 8 months ago

Log in to reply

Yes..I considered only 2 digit numbers. I need to know how it works!

ASHWIN K - 3 years, 8 months ago

Log in to reply

After you know that b=9b=9, what happens when you substitute b=9b=9 into the equation ab+a+b=10a+bab + a +b = 10a + b?

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh consider any single digit value for a,

For instance a =1, the equation becomes 1*9 + 1 + 9 = 19 = 10(1) + 9 = 19.

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K You can do that as well for a=2,3,,9a=2,3,\ldots,9, but that is tiresome.

I asked you to substitute b=9b=9 alone only, nothing else. What happens to the equation ab+ab+b=10a+bab+ab+b=10a+b after you substitute b=9b=9?

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh Got you. both side equations are becoming equal. Can we extend this for 3 digit numbers. Do u have any idea?

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K Hmmm, yes we can, by assuming your last digit is already given, then you can make up any equation as you like. But I doubt any of these identity are useful, because it is too specific and are not applicable in the first place.

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh 9 always been a magic number. Knowing it's property will always be handy. I made up this note after solving a problem of this kind.

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K No, it's not. What is so special about 9?

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh It is magical number because we consider base 10 in our number system and thus last number '9' has to be Special. In general, last digit in that number system will carry special properties.

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K That made no sense, I could call the number 8 special because "the second last number '8' has to be special".

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh There are interesting properties on it buddy. This is not my judgement. I think I am not convincing you. Just Google it for yourselves and check.

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K The number 8 also has interesting properties.

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh Wow..let me know that.

ASHWIN K - 3 years, 8 months ago

Log in to reply

@Ashwin K Read up application of divisibility rules.

Pi Han Goh - 3 years, 8 months ago

Log in to reply

@Pi Han Goh Cool..I agree all numbers got it's own properties.

ASHWIN K - 3 years, 8 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...