perplexus.info :: Tricks : Proving a witch weighs the same as a duck

Proving a witch weighs the same as a duck (Posted on 2005-02-21)

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?

Submitted by Dustin

Rating: 3.0000 (4 votes)

Solution: (Hide)

From (W-A)^2 = (D-A)^2 to (W-A) = (D-A).
Assuming the witch weighs more than the duck, the average weight(A) is greater than the duck's weight(D) and less than the witch's(W).
So W-A is positive, while D-A is negative. It's like trying to prove 3=-3 because they are both the square root of 9.
I could take the square root, but it would end up (W-A) = (-D+A). Adding A to both sides gives 1).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-07-16 22:13:28
re(3): Monty Python logical method	Bruce Brantley	2005-02-24 14:53:24
Possible solution	Robyn	2005-02-24 01:10:08
re(2): Monty Python logical method	Larry	2005-02-23 11:37:05
It's elementary (elementary math)	Penny	2005-02-22 21:17:31
re: Monty Python logical method	Bruce Brantley	2005-02-22 18:02:45
PERHAPS	Rex	2005-02-22 14:40:02
Monty Python logical method	Larry	2005-02-22 02:40:16
some thoughts	momo	2005-02-21 16:30:53
Solution	np_rt	2005-02-21 16:25:08
solution	joseph	2005-02-21 15:19:59
Spoiler	Steve Herman	2005-02-21 15:08:00
Who says they don't weight the same? (solution)	Jer	2005-02-21 15:05:24

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