Question: You have 9 squares with side lengths 1,2,3,4,5,6,7,8,9. What is the smallest rectangle you can put them in? (smallest meaning smallest in area, and you put them in without overlap) A rectangle with area 1^2+...+9^2 won't work. Is there a standard technique for going at this type of question? I can make a pretty good stab at it, just by trial and error, and I'm fairly convinced I have the best possible, but how does one prove such a thing? Is there a general way to go about this with side lengths 1,2,3,....,n, or even with some random set of squares? Gary McGuire
Gary McGuire wrote:
You have 9 squares with side lengths 1,2,3,4,5,6,7,8,9. What is the smallest rectangle [in area] you can put them in?
If you mayn't tilt the squares, 20x15. Here's one way. 22..7777777999999999 22..7777777999999999 44447777777999999999 44447777777999999999 44447777777999999999 44447777777999999999 ....7777777999999999 88888888333999999999 88888888333999999999 88888888333..666666. 8888888855555666666. 8888888855555666666. 8888888855555666666. 8888888855555666666. 88888888555556666661
Is there a standard technique for going at this type of question? Is there a general way to go about this with side lengths 1,2,3,....,n, or even with some random set of squares?
Exhaustive search. Anyone know a better way? -- Don Reble djr@nk.ca
OMG, you're going to have Eric Friedman and Ed Pegg busy now. ----- Original Message ----- From: "Gary McGuire" <Gary.McGuire@nuim.ie> To: <ham>; <math-fun@mailman.xmission.com> Sent: Thursday, February 24, 2005 3:26 PM Subject: [math-fun] squares
Question:
You have 9 squares with side lengths 1,2,3,4,5,6,7,8,9. What is the smallest rectangle you can put them in?
-- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.300 / Virus Database: 266.4.0 - Release Date: 2/22/2005
It's easy if you follow the now standard solving technique. 1. Make the start of the sequence. 2. Look the sequence up at OEIS. In this case, http://www.research.att.com/projects/OEIS?Anum=A081287 Lots more on the topic is at http://www.maa.org/editorial/mathgames/mathgames_12_01_03.html Ed Pegg Jr --- David Wilson <davidwwilson@comcast.net> wrote:
OMG, you're going to have Eric Friedman and Ed Pegg busy now.
----- Original Message ----- From: "Gary McGuire" <Gary.McGuire@nuim.ie> To: <ham>; <math-fun@mailman.xmission.com> Sent: Thursday, February 24, 2005 3:26 PM Subject: [math-fun] squares
Question:
You have 9 squares with side lengths 1,2,3,4,5,6,7,8,9. What is the smallest rectangle you can put them in?
-- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.300 / Virus Database: 266.4.0 - Release Date: 2/22/2005
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participants (4)
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David Wilson -
Don Reble -
ed pegg -
Gary McGuire