# 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. – GOTO 0 Apr 19 '15 at 17:57
• ah really ??? you divide by 0 ??? iron man should be blown up laughing at that – Abr001am Apr 19 '15 at 19:22
• @A_E Why did you remove the tags #paradox and #word-problem? – leoll2 Apr 19 '15 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 '15 at 20:13
• @A_E Word-problem isn't word. It simply means that the problem is dressed with a story – leoll2 Apr 19 '15 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. – Milo Brandt Apr 20 '15 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