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From: gayde@iwu1b.UUCP (Peter Gayde)
Newsgroups: net.math
Subject: Math for Smart Alecks
Message-ID: <114@iwu1b.UUCP>
Date: Fri, 27-Jan-84 09:48:53 EST
Article-I.D.: iwu1b.114
Posted: Fri Jan 27 09:48:53 1984
Date-Received: Sat, 28-Jan-84 02:46:24 EST
Organization: AT&T Bell Labs, Naperville, IL
Lines: 36

I saw this recently in GAMES magazine.  I didn't believe it at first,
but after many attempts I could only sit back and wonder why it works.

1. Take ANY two numbers: say, 116 and 3011.
2. Halve the first number again and again, discarding any fractional
   remainder, until you reach 1.  Thus: 116, 58, 29, 14, 7, 3, 1.
3. Double the second number as many times as you halved the first.
   Thus: 3011, 6022, 12044, 24088, 48176, 96352, 192704.
4. Write these series alongside each other, and cross out every even
   number in the HALVES column and its partner in the DOUBLES column.
   Thus, as shown below, the even numbers in the HALVES column (116,
   58 and 14) are crossed out along with their companions in the
   DOUBLES column (3011, 6022 and 24088) REGARDLESS OF WHETHER THESE
   ARE EVEN OR ODD.

	HALVES		DOUBLES
	 116	 xxx	  3011
	 58	 xxx	  6022
	 29		 12044
	 14	 xxx	 24088
	  7		 48176
	  3		 96352
	  1		192704

5. Add the numbers that remain in the DOUBLES COLUMN ONLY.  The
   resulting sum will be equal to the product of the two numbers you
   started with.

   12044 + 48176 + 96352 + 192704 = 349276 = 116 x 3011 !!!!!!!

Does anyone have any inkling as to why this works?
-- 
	Peter Gayde	ihnp4!{iwu1b,ihuxp}!gayde
	AT&T Technologies
	Naperville, IL
	(312) 979-7186