Is it this lengthy?

I was doing this problem today:

https://brilliant.org/problems/its-easy-isnt-it/

First of all attempt the problem before proceeding further in this note. Got it? A lengthy solution?

Oh yes, I also figured it out after 30 mins (by solving cases). But this forced me to ponder that is there a short-and-sweet solution to this problem? Please tell me in the comments if you found one.

#Algebra

Easy Math Editor

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Comments

Even I solved it by checking cases.......see the solution,....that also solves it the same way......But I don't see how you spent 30 minutes on this........maybe practicing enough questions will increase your speed.......:)

Aaghaz Mahajan - 2 years ago

30 mins was just a guess..

Aaryan Maheshwari - 2 years ago

This is a very nice solution. As it turns out, each x in the absolute value will have maximum of 2 integer solutions. Since there are 3 x's in absolute value, there is 3 x 2 solutions: so 6 solutions is the complete total. I hope that was helpful, because this approach takes 15 seconds.

Dacota Sprague - 1 year, 12 months ago

I've posted my approach.

Pi Han Goh - 1 year, 11 months ago

Math	Appears 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}`	$\boxed{123}$