# Number Jumping (notes)

This note came from https://brilliant.org/practice/number-jumping-i/?chapter=gcd-and-lcm and if you don’t understand what the math behind it means, this is the note you’re looking for. I recommend to click the link and finish the quiz before coming back.

Example:
Ryan has two numbers; 9 and 14. He can add 9 or subtract 9. He can also do the same with 14. Can he get to any number he wanted with just those two numbers (including negative just for fun)?

This problem is relatively easy, if you know how to solve it. All you need to do is find the G.C.D. (A.KA. Greatest Common Divisor). 9 has factors of 1, 3, and 9. 14 has factors of 1, 2, 7, and 14. The G.C.D. Of 9 and 14 is 1, so:
Yes, Ryan can reach any number he wanted (again, including negative).

Still confused, well here’s a simple math equation to clear up confusion:
(9x3) - (14x2) = 1

The same thing can be done for negative numbers:
(9x-3) + (14x2) = -1

And from there, you can add or subtract -1 to -1 continuously, and you will cover up all the numbers. the opposite is also true with 1.

Now you can use that knowledge to solve my sequel quiz to this note:
https://brilliant.org/problems/number-jumping-a-follow-up-problem-to-number/

P.S.: If I can reach #10 or higher on new quizzes, then I will post a not about Python followed by a quiz about it a few days after. (not the giant snake Apollo slain at least 2 times already) (the coding language). Also, it’s in the new section as well as the number theory section.

Note by Ash Ketchup
4 months, 4 weeks 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:

If you can’t seem to get into the link, just copy and paste it.

- 4 months, 4 weeks ago

Also, I will know if the problem is #10+ on popular, because I will check every day.

- 4 months, 4 weeks ago

Kidding right? Like and sub!

- 4 months, 3 weeks ago

Bincky will not know how to solve this: I got bincky from Percy jackson

- 4 months, 3 weeks ago

Hello there, are you the person who just happened to have said my name?

- 4 months, 3 weeks ago

Do you know the book?

- 4 months, 3 weeks ago

No offense

- 4 months, 3 weeks ago

Why would I be offended?

- 4 months, 3 weeks ago

Well Percy Jackson is kind of a cartoon to me but I still like reading it

- 4 months, 3 weeks ago

Cartoon lol 😆😆😆😆😆😆😆😆😆

- 4 months, 3 weeks ago

Yes I do. What do you mean by 'bincky'?

- 4 months, 3 weeks ago

Biancia

- 4 months, 3 weeks ago

I mean the character

- 4 months, 3 weeks ago

That kinda died because of Peter johnson

- 4 months, 3 weeks ago

Umm ‘Peter jhonson?’

- 4 months, 3 weeks ago

‘Peter Johnson

- 4 months, 3 weeks ago

A.K.A. Percy Jackson or as Dionysus would put it, “Whatever...”

- 4 months, 3 weeks ago

Percy jackson

- 4 months, 3 weeks ago

Wat pahry

- 4 months, 3 weeks ago

Nevermind...

- 4 months, 3 weeks ago

I believe the answers to the "math equation" examples were switched. The first equals $-1$, the second, $1$.

Very clever solution!

- 4 months, 3 weeks ago

@David Stiff oh okay I will correct it immediately

- 4 months, 3 weeks ago

Thanks for pointing out the mistake

- 4 months, 3 weeks ago

No problem!

- 4 months, 3 weeks ago

David Stiff - 2 days, 5 hours ago

- 4 months, 3 weeks ago

:)

- 4 months, 3 weeks ago

Lol

- 4 months, 3 weeks ago