# Obi-Wan vs Grievous

19 BBY, the Galactic Republic spots General Grievous in Utapau, the Separatists' Council Base; the Jedi Obi-Wan Kenobi is sent there to deal with him.
After a long search, Obi-Wan comes face to face with the Supreme Commander:

Obi-Wan: Surrender, it's over!
Grievous: Mwhahaha, fool! How can you beat me?!?!
Obi-Wan: With my lightsaber, of course!
Grievous: Mwhahaha, have you ever seen my set of four lightsabers?
Obi-Wan: Do you feel advantaged? May the math be with you! There's no difference between one and four!
Grievous: Can you prove it?
Obi-Wan:
$x=4$
$x(x-1)=4(x-1)$
$x^2-x=4x-4$
$x^2-4x=x-4$
$x(x-4)=x-4$
$x=1$
Grievous: You're trying to use the Force on me, but it won't work!

Is Obi-Wan's math as strong as his Force? Explain it!

If you like problems like this, check A dollar, a penny, there's no difference

• Reminds me of 2=3. Apr 19, 2015 at 17:57
• ah really ??? you divide by 0 ??? iron man should be blown up laughing at that Apr 19, 2015 at 19:22
• @A_E Why did you remove the tags #paradox and #word-problem? Apr 19, 2015 at 19:50
• Hi @leoll2, 'paradox' or 'brainteaser' seemed like they might fit but I'm really struggling to see how 'word-problem' or 'riddle' could. Others may disagree....
– A E
Apr 19, 2015 at 20:13
• @A_E Word-problem isn't word. It simply means that the problem is dressed with a story Apr 19, 2015 at 20:19

When you multiplied both sides by $(x-1)$, you introduced the new extraneous solution $x=1$ to the equation. Later on when you divided by $(x-4)$, you forgot to case check that $(x-4)$ might equal $0$. If we do so we get $x = 1$ or $4$, as expected.

We started by specifying $x=4$. Making this substitution makes the error more clear: \begin{align} 4&=4\\ &\vdots\\ 4(4-4)&=(4-4)\\ 4&=1 \end{align} The second to last line is true, but the last isn't, because we divided by $4-4=0$.

Multiplying LHS and RHS by zero(if $x=1,x-1=0$) can equate any non-equal equations, So Obi-Wan did solve wrongly.

And the thing if any equation has 2 roots, say, $x_1,x_2$, that imply $either~x_1~or~x_2~or~both$ has solution.(i.e. He can't say both are solution)

For Example:- $ax=bx$ implies $a=b$, if, and only if, $x\neq 0$

Obi-Wan's math is not nearly as strong as his force. His math breaks at two different points based on whether we consider x=4 or x=1:

if x=1:

Line 2: x(x−1)=4(x−1) breaks the proof because were saying 0=0, so the rest of the proof is essentially void.

if x=4:

Line 5: x(x−4)=x−4 going to Line 6: x=1 is invalid because we are dividing by zero

Either way, Obi-Wan's math was not strong enough to fool Grievous

• It's worth noting that the issues you point out are in different directions; line 6 does not follow from line 5, and line 1 does not follow from line 2. However, if we only care about the forward direction (which seems to be the case), the proof is fine up to line 5. Apr 20, 2015 at 2:37

the trick is in these two lines:

$$x(x−4)=x−4$$ $$x=1$$

$x(x−4)=x−4$ is a second degree equation which has for solutions $x=1$ OR $4$

You cant deduce directly $x=1$ without a specific reason this is maths not lottery