Comments on: How many times must you cut a gold bar that is 31 cm long for the pieces to all be the same? http://goldinflorence.com/523/how-many-times-must-you-cut-a-gold-bar-that-is-31-cm-long-for-the-pieces-to-all-be-the-same/ Gold Discussion Board Fri, 30 Jul 2010 22:53:27 +0000 http://wordpress.org/?v=2.8.2 hourly 1 By: Mike N http://goldinflorence.com/523/how-many-times-must-you-cut-a-gold-bar-that-is-31-cm-long-for-the-pieces-to-all-be-the-same/comment-page-1/#comment-2038 Mike N Mon, 23 Feb 2009 17:54:17 +0000 http://goldinflorence.com/?p=523#comment-2038 binary --> 1,2,4,8, 16 binary –> 1,2,4,8, 16

]]> By: Puzzling http://goldinflorence.com/523/how-many-times-must-you-cut-a-gold-bar-that-is-31-cm-long-for-the-pieces-to-all-be-the-same/comment-page-1/#comment-2037 Puzzling Fri, 20 Feb 2009 17:10:35 +0000 http://goldinflorence.com/?p=523#comment-2037 Make segments in these lengths: 1, 2, 4, 8 and 16 With these you can use binary addition to make any number from 1 to 31. Example: 1 = 1 2 = 2 2+1 = 3 4 = 4 4+1 = 5 4+2 = 6 4+2+1 = 7 8 = 8 8+1 = 9 8+2 = 10 8+2+1 = 11 8+4 = 12 8+4+1 = 13 8+4+2 = 14 8+4+2+1 = 15 16 = 16 16+1 = 17 etc. Answer: You need only *4* cuts to make these lengths. Make segments in these lengths:
1, 2, 4, 8 and 16

With these you can use binary addition to make any number from 1 to 31.

Example:
1 = 1
2 = 2
2+1 = 3
4 = 4
4+1 = 5
4+2 = 6
4+2+1 = 7
8 = 8
8+1 = 9
8+2 = 10
8+2+1 = 11
8+4 = 12
8+4+1 = 13
8+4+2 = 14
8+4+2+1 = 15
16 = 16
16+1 = 17
etc.

Answer:
You need only *4* cuts to make these lengths.

]]> By: prime3079 http://goldinflorence.com/523/how-many-times-must-you-cut-a-gold-bar-that-is-31-cm-long-for-the-pieces-to-all-be-the-same/comment-page-1/#comment-2036 prime3079 Tue, 17 Feb 2009 20:00:19 +0000 http://goldinflorence.com/?p=523#comment-2036 The only way to have whole numbers is when its divided by 31 and this means you would need to make 30 cuts 30 31 and this means you would need to have whole numbers is when its divided by 31 and this means you. The only way to make 30 31 and this means you would need to make 30 cuts 30 31. The only way to have whole numbers is when its divided by 31 and this means you would need to make 30 cuts 30 31 and this means you would need to have whole numbers is when its divided by 31 and this means you.
The only way to make 30 31 and this means you would need to make 30 cuts 30 31.

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