Suppose the witch weighs W pounds, and the duck weighs D pounds. Also, suppose their average weight is A pounds. (Their combined weight is 2A)

W + D = 2A. (Given)
W = 2A - D. (Subtract D)
W - 2A = -D (Subtract 2A)
W(W - 2A) = W(-D) (Multiply by W)
W(W - 2A) = (2A - D)(-D) (Substitute 2A-D for W using the given equation)
W² - 2AW = -2AD + D² (Distribute)
W² - 2AW + A² = D² - 2AD + A² (Add A²)
(W-A)(W-A)=(D-A)(D-A). (Factor)
(W-A)² = (D-A)². (An expression times itself equals the expression squared)
(W-A) = (D-A) (Square root)
W = D (Add A)

In other words, a witch weighs the same as a duck.

Where did I go wrong?

A village. Sound of chanting of Latin canon, punctuated by short,
sharp cracks. It comes nearer. We see it is a line of MONKS ala
SEVENTH SEAL flagellation scene, chanting and banging themselves on the foreheads with wooden boards. They pass a group of villagers who are dragging a beautiful YOUNG WOMAN dressed as a witch through the streets. They drag her to a strange house/ruin standing on a hill outside the village. A strange-looking knight stands outside, SIR BEDEVERE.
FIRST VILLAGER
We have found a witch. May we burn her?
ALL
A Witch! Burn her!
BEDEVERE
How do you know she is a witch?
ALL
She looks like one. Yes, she does.
BEDEVERE
Bring her forward.
They bring her forward - a beautiful YOUNG GIRL (MISS ISLINGTON) dressed up as a witch.
WITCH
I am not a witch. I am not a witch.
BEDEVERE
But you are dressed as one.
WITCH
They dressed me up like this.
ALL
We didn't, we didn't!
WITCH
This is not my nose, It is a false one.
BEDEVERE takes her nose off.
BEDEVERE
Well?
FIRST VILLAGER
... Well, we did do the nose.
BEDEVERE
The nose?
FIRST VILLAGER
And the hat. But she is a witch.
ALL
A witch, a witch, burn her!
BEDEVERE
Did you dress her up like this?
FIRST VILLAGER
... Um ... Yes ... no ... a bit ... yes... she has got a wart.
BEDEVERE
Why do you think she is a witch?
SECOND VILLAGER
She turned me into a newt.
BEDEVERE
A newt?
SECOND VILLAGER
(After looking at himself for some time) I got better.
ALL
Burn her anyway.
BEDEVERE
Quiet! Quiet! There are ways of telling whether she is a witch.
ARTHUR and PATSY ride up at this point and watch what follows with interest
ALL
There are? Tell up. What are they, wise Sir Bedevere?
BEDEVERE
Tell me ... what do you do with witches?
ALL
Burn them.
BEDEVERE
And what do you burn, apart from witches?
FOURTH VILLAGER
... Wood?
BEDEVERE
So why do witches burn?
SECOND VILLAGER
(pianissimo)
... Because they're made of wood...?
BEDEVERE
Good.
PEASANTS stir uneasily then come round to this conclusion.
ALL
I see. Yes, of course.
BEDEVERE
So how can we tell if she is made of wood?
FIRST VILLAGER
Make a bridge out of her.
BEDEVERE
Ah ... but can you not also make bridges out of stone?
ALL
Ah. Yes, of course ... um ... err ...
BEDEVERE
Does wood sink in water?
ALL
No, no, It floats. Throw her in the pond Tie weights on her. To the pond.
BEDEVERE
Wait. Wait ... tell me, what also floats on water?
ALL
Bread? No, no, no. Apples .... gravy ... very small rocks ...
ARTHUR
A duck.
They all turn and look at ARTHUR. BEDEVERE looks up very impressed.
BEDEVERE
Exactly. So... logically ...
FIRST VILLAGER
(beginning to pick up the thread)
If she ... weighs the same as a duck ... she's made of wood.
BEDEVERE
And therefore?
ALL
A witch! ... A duck! A duck! Fetch a duck.
FOURTH VILLAGER
Here is a duck, Sir Bedevere.
BEDEVERE
We shall use my largest scales.
He leads them a few yards to a very strange contraption indeed, made of wood and rope and leather. They put the GIRL in one pan and the duck in another. Each pan is supported by a wooden stave. BEDEVERE checks each pan then ... ARTHUR looks on with interest.
BEDEVERE
Remove the supports.
Two PEASANTS knock them away with sledge hammers. The GIRL and the duck swing slightly but balance perfectly.
ALL
A witch! A witch!
WITCH
It's a fair cop.
All
Burn her! Burn her! Let's make her into a ladder.
The VILLAGERS drag the girl away, leaving ARTHUR and BEDEVERE regarding each other admiringly.
BEDEVERE
Who are you who are so wise in the ways of science?
ARTHUR
I am Arthur, King of the Britons.

Posted by Larry on 2005-02-22 02:40:16