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 2009-11-11, 18:46 #1 Flatlander I quite division it     "Chris" Feb 2005 England 31×67 Posts Chocolate You have a bar of chocolate that has 32 squares arranged as 4 x 8. What is the minimum number of breaks that will turn this into its individual squares? Rules: No melting, freezing, cutting, sawing, use of ultrasound, WMDs, particle accelerators etc. Snapping with the fingers in the traditional manner only. I will not accept responsibility for any injury, death, loss etc. Last fiddled with by Flatlander on 2009-11-11 at 18:47
2009-11-11, 18:54   #2
R.D. Silverman

Nov 2003

746010 Posts

Quote:
 Originally Posted by Flatlander You have a bar of chocolate that has 32 squares arranged as 4 x 8. What is the minimum number of breaks that will turn this into its individual squares? Rules: No melting, freezing, cutting, sawing, use of ultrasound, WMDs, particle accelerators etc. Snapping with the fingers in the traditional manner only. I will not accept responsibility for any injury, death, loss etc.
The problem is not well posed. For example, suppose I break it
with one break into two 4x4 squares. Can I then place one on top
of the other and do another break (i.e. break both at once) to
get 4 2x4 rectangles? Can I then stack them and break again? etc.

 2009-11-11, 19:01 #3 Flatlander I quite division it     "Chris" Feb 2005 England 207710 Posts No 'stacking' allowed.
 2009-11-11, 19:05 #4 Dougal     Jan 2009 Ireland 18610 Posts Bob, i was thinking the same thing. Whats the saying, Great minds think alike. my guess,just working it out in my head is 31
2009-11-11, 19:10   #5
CRGreathouse

Aug 2006

3×1,993 Posts

Quote:
 Originally Posted by Flatlander No 'stacking' allowed.
So if the first move was to make two 4x4s, the second move would be required to be splitting a 4x4 into two 2x4s?

 2009-11-11, 19:14 #6 bsquared     "Ben" Feb 2007 29·7 Posts How big are the squares? If the bar is appreciably bigger than my hand then I probably couldn't do it with my guess below. 10
 2009-11-11, 19:16 #7 lfm     Jul 2006 Calgary 52·17 Posts 31
2009-11-11, 19:17   #8
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by Flatlander No 'stacking' allowed.
That's too bad. I like them stacked.

 2009-11-11, 20:43 #9 S485122     "Jacob" Sep 2006 Brussels, Belgium 32×197 Posts What is a "break" ? Even without stacking if one takes the bar in hands and pushes on a inner square, in one movement there are many fractures... If a "break" of one piece results in two pieces only, I agree the answer should be 31. Jacob
 2009-11-11, 21:14 #10 Flatlander I quite division it     "Chris" Feb 2005 England 31×67 Posts I meant a clean, straight-line break. But I think this has run its course now. There are at least 4 conclusions: 1) Each clean, straight-line break results in one more piece. So the answer is 31. (Which is annoying and why I don't share my chocolate.) 2) Generous mathematicians have broken nails and strong hands from repeatedly trying to use the optimum 'Binary Method'. 3) They consider this to be "the traditional manner". 4) Defining a well posed puzzle is quite hard.
 2009-11-12, 00:58 #11 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 22×3×17×31 Posts I find that sticking a bar in my back pocket and then sitting down tends to create many pieces in just one 'breaking event'. And later, sitting on a radiator long enough will put it back into 'one piece' again.

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