0

What is the maximum number of pieces that a pizza can be cut into by $7$ knife strokes?

David G. Stork
  • 29,774
Picaso
  • 504
  • You must have tried something yourself .... Any thoughts? – Bram28 Aug 14 '17 at 21:48
  • isn't $2^7=128$. – hamam_Abdallah Aug 14 '17 at 21:48
  • 1
    @lulu 'possible' duplicate? :) I wonder why it's always 7 .... – Bram28 Aug 14 '17 at 21:49
  • @Salahamam_Fatima Only if it is allowed to replace th pizza slices after each cut, e.g. stacking them. – M. Winter Aug 14 '17 at 21:50
  • @Bram28:I thought about this,but i got confused after while.... – Picaso Aug 14 '17 at 21:51
  • And if you can fold the pizza any which way, the number goes way up ..... infinity I suppose? – Bram28 Aug 14 '17 at 21:51
  • 1
    You'll have to define a 'knife stroke'. If a stroke can zig-zag, then even two strokes is enough to cut the pizza into arbitrarily many pieces. – MPW Aug 14 '17 at 21:52
  • @Bram28:This question was asked by my friend,we tried it even by making pictures,but there arised infinite possiblities of cutting – Picaso Aug 14 '17 at 21:53
  • @Picaso OK, it's always good to just start with smaller numbers and see if a pattern emerges ... so start with 1 cut ... 2 slices. 2 cuts ... maximum of 4 slices (2 more) ... 3 cuts: 7 slices (3 more) .. 4 cuts: 11 slices (4 more) ... any pattern yet? – Bram28 Aug 14 '17 at 21:53
  • @MPW:You explained my problem perfectly:-) – Picaso Aug 14 '17 at 21:53
  • The problem becomes more tractable if you limit a knife stroke to being a line segment – MPW Aug 14 '17 at 21:55
  • @https://math.stackexchange.com/questions/1657081/maximum-number-of-pieces-of-pizza-when-making-7-cuts Please explain me how the third stroke divides the pizza into 7 parts.I tried it by making picture,i'm getting 6 parts ?i'm cutting by concurrent lines with intersection point at the cente of pizza. – Picaso Aug 14 '17 at 21:59
  • @Picaso assume the first two strokes go through the center of the circle. The third cut must be off center but if pretty close to center will leave a little triangle with one vertex at the center of the circle. The other 6 pieces will surround the little piece. In other words the third stroke must go 3 of the 4 pieces left after the first two strokes. (And the fourth stroke will go through 4 of those 7, the fifth through 5 of those 11, etc.) – Χpẘ Aug 14 '17 at 22:04
  • @Picaso Make sure that every new cut goes through all the other cuts but at different points. So you never want three or more cuts all intersecting in the same point. Here is a pic with 4 cuts: http://www.basic-mathematics.com/images/11-pieces-pizza.gif.pagespeed.ce.8eQlEx8WuK.gif – Bram28 Aug 14 '17 at 22:06
  • It's kind of interesting to think about this problem in relation to the 4 color map problem (if it were limited to straight lines as borders). – Χpẘ Aug 14 '17 at 22:10
  • @Bram28:Got it !!!thanks – Picaso Aug 14 '17 at 22:14
  • Thank you guys!!!!For a great discussion. – Picaso Aug 14 '17 at 22:15
  • @Picaso You're welcome! :) – Bram28 Aug 14 '17 at 22:23

0 Answers0