bonanova Posted March 23, 2008 Report Share Posted March 23, 2008 Using a knife to make four straight-line cuts, how many pieces can a single pancake be divided into? Generalize for N cuts. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 (edited) Using a knife to make four straight-line cuts, how many pieces can a single pancake be divided into? Generalize for N cuts. I think 11 pieces... But not sure how to generalize. Edited March 23, 2008 by Noct Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Easy: 4 cuts would give us 8 pieces. To generalise ==> N * 2 = Number of pieces. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Easy: 4 cuts would give us 8 pieces. To generalise ==> N * 2 = Number of pieces. You can get more than that. Can you think of a way how? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 23, 2008 Author Report Share Posted March 23, 2008 What happens on the first cut? The Nth cut? Induction. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 You can get more than that. Can you think of a way how? Sure we can(10), but they wont be equal sizes and we will not be able to genralise it to N cuts. Circle -> 2 horizontal straight lines one on top and one at the bottom. Now draw and X thus we have 4 straight lines and 10 pieces. But they will not be equal and will not be sectors, they will be different shapes. Let me know if there is a way to get more than 10 with 4 straight line cuts. Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 23, 2008 Author Report Share Posted March 23, 2008 Sure we can(10), but they wont be equal sizes and we will not be able to genralise it to N cuts. Circle -> 2 horizontal straight lines one on top and one at the bottom. Now draw and X thus we have 4 straight lines and 10 pieces. But they will not be equal and will not be sectors, they will be different shapes. Let me know if there is a way to get more than 10 with 4 straight line cuts. If I had to share the pancake, I'd want to do the cutting. Think about the placement of the last cut.The OP does not requre them to be equal size. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 (edited) with 4 straight line: 11 pieces. Generalized: if n is the number of lines and f(n) is the number of pieces, then f(n)=f(n-1)+n; where, f(0)=1; results: 0 line--> 1 piece 1 line--> 2 pieces 2 lines --> 4 pieces 3 lines--> 7 pieces 4 lines--> 11 pieces 5 lines--> 16 pieces 6 lines-->22 pieces : : Edited March 23, 2008 by storm Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 If I had to share the pancake, I'd want to do the cutting. Think about the placement of the last cut.The OP does not requre them to be equal size. Got it. 11 pieces it is. Wow ...shows that I know lesser than I thought I knew about functions. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Hi storm. Can you show your answer graphically like what chanakyavq did? hheh Quote Link to comment Share on other sites More sharing options...
0 grey cells Posted March 23, 2008 Report Share Posted March 23, 2008 (edited) Finally , figured out the max. no. of pieces. Figured it out from Storm's generalised formula. (Initially figured it out as 10) Edited March 23, 2008 by grey cells Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Using a knife to make four straight-line cuts, how many pieces can a single pancake be divided into? Generalize for N cuts. Roll the pancake first (actually after adding the sugar lemon and berries - heck just eat it) If you don't eat it but cut it four times first - then in a rolled condition how many pieces do you get! I guess size matters! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 (edited) Hi storm. Can you show your answer graphically like what chanakyavq did? hheh here u go. if you notice the pieces are not equal and some are very small. but according to the problem, it does not mention that they need to be equal. So we get 11 pieces. Edited March 23, 2008 by chanakyavg Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Chanakyavq...thanks so much...now i dont just imagine it, but see it..hehhehe..thanks again Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 I disagree with LIS it should be peach sauce and icecream Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 Not as good as previous with 16, but 14 by cutting pancake similar to the way guy with four cuts did before (remove 1 o'clock to 8 o'clock cut), gets you 7 pieces. Then cut into top and bottom and you have 14 pieces. Quote Link to comment Share on other sites More sharing options...
0 itachi-san Posted March 23, 2008 Report Share Posted March 23, 2008 Stack the pieces after each cut (assuming they don't crumble apart) you get 16 pieces. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 23, 2008 Report Share Posted March 23, 2008 I disagree with LIS it should be peach sauce and icecream eerst kaas en spek.... lekker! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 24, 2008 Report Share Posted March 24, 2008 (edited) 16 if you stack each piece after cutting them Edited March 24, 2008 by Jordanmax Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 24, 2008 Report Share Posted March 24, 2008 (edited) Hi storm. Can you show your answer graphically like what chanakyavq did? hheh I have already shown the generalized form...for graphical...cilck spoiler Here it is.. Edited March 24, 2008 by storm Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted March 24, 2008 Author Report Share Posted March 24, 2008 A verbal form of storm's equation is to note that the Nth cut will add N new pieces if it crosses all the previous cuts. Note in the previous sketch that gave an answer of 10, the final cut failed to cross exactly one of the previous cuts. Quote Link to comment Share on other sites More sharing options...
0 itachi-san Posted March 24, 2008 Report Share Posted March 24, 2008 I think people are missing the stacking idea i posted. You get 16 that way. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 25, 2008 Report Share Posted March 25, 2008 I think people are missing the stacking idea i posted. You get 16 that way. People are not interested.. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 25, 2008 Report Share Posted March 25, 2008 People are not interested.. i am - bot not that much It was a good idea - better than storms, settle down - its only a puzzle, no one to beat but yourself. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 25, 2008 Report Share Posted March 25, 2008 Here is my answer with four cuts we can get 14 pieces. It goes like 1 cut 2 pieces 2 cut 4 pieces 3 cut 7 pieces 4 cut 14 pieces(cut from side) 5 cut 25 pieces(again from side but slightly angeled) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 25, 2008 Report Share Posted March 25, 2008 eerst kaas en spek.... lekker! doorna perzik en roomijs -lekker! Quote Link to comment Share on other sites More sharing options...
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bonanova
Using a knife to make four straight-line cuts,
how many pieces can a single pancake be divided into?
Generalize for N cuts.
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