Gold Bar: A gold bar is exactly 31 centimeters long. If you want to divide the bar into smaller segments so that one or a combination of segments can add up to every whole number of centimeters from 1 to 31, how many cuts must you make?
Patty
February 17, 2009
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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.
Comment by prime3079 — February 17, 2009 @ 8:00 pm
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.
Comment by Puzzling — February 20, 2009 @ 5:10 pm
binary –> 1,2,4,8, 16
Comment by Mike N — February 23, 2009 @ 5:54 pm