From ziggy@hx.lcs.mit.edu Wed Oct  2 20:11:28 1991
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Date: Wed, 2 Oct 91 19:04:54 EDT
From: ziggy@hx.lcs.mit.edu (Michael R. Blair)
To: 6001-staff@ai.mit.edu
Subject: Interesting snippet...

>From reistad@cronkite.LCS.MIT.EDU Wed Oct  2 15:16:56 1991
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Date: Wed, 2 Oct 91 15:16:37 EDT
From: reistad@cronkite.LCS.MIT.EDU (Brian Reistad)
Message-Id: <9110021916.AA04605@cronkite.LCS.MIT.EDU>
To: ziggy@hx.lcs.mit.edu
Subject: PS2-improve3 soln
Status: RO



Consider this soln for PS.improve3 found by two of my students:

Given guess want to find value for n which generated guess:
	guess = n^2 + n + 41
Soln: Consider 4*guess  = 4n^2 + 4n + 164
			= 4n^2 + 4n + 1 + 163
			= (2n+1)^2 + 163
	
	(2n+1)^2 = 4guess - 163
	
	2n+1 = sqrt(4guess-163)

	2n = sqrt(4guess-163) - 1

	n = (sqrt(4guess-163) - 1) / 2

(define (improve3 guess)
    (let ((n (/ (- (sqrt (- (* 4 guess) 163)) 1) 2)))
	(+ (square (+ n 1)) (+ n 1) 41)))


--Brian



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I personally would get a kick out of seeing more ducky messages like this.
Thanks brian!

 ziggy


