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    • Slice being taken out of cake

      Sharing cakes

      3 February, 2020

      We'd like to thank Syed Abbas, Associate Professor and Chairperson SBS, IIT Mandi, India, for sending in this puzzle. Reportedly, a version of it was put to Ali ibn Abi Talib in the seventh century AD. Another version appears in Fibonacci's famous Liber Abaci.


      Cake

      Two people on a long walk sit down for a well-deserved break. Person A has brought along 3 cakes to eat and person B has brought along 5 cakes.

      As they are just about to tuck in person C arrives and asks to share their meal. A and B agree. They cut each cake into three equal pieces and each person eats one piece of each cake.

      After the meal person C pays 8 coins for the cake. Person A gives 5 of these coins to person B and keeps 3 for himself. But person B complains. She demands to be given 7 of the coins with only 1 remaining for A.

      Who is right and why?

      Can you generalise the solution for an initial k people having n1,n2,...,nk cakes respectively, who are then joined by another m people who pay n1+n2+n3+...+nk coins each?

      Solution link
      Sharing cake: Solution
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      Maths guy

      10 March 2023

      Permalink
      Comment

      I think that person A is correct as each coin should contribute to a cake

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      Comment

      29 March 2023

      In reply to Answer by Maths guy

      Permalink
      Comment

      I think person A in corect as each coin should be worth a cake.

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      Comment

      29 March 2023

      In reply to Answer by Maths guy

      Permalink
      Comment

      Person A is right because each coin should equal 1 slice.

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      Janvi

      1 July 2023

      In reply to Math by Comment

      Permalink
      Comment

      No bro
      A person also eats 2 extra slice from person b so he should give him 2 coins extra

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      Neel S

      23 April 2023

      Permalink
      Comment

      Person c paid 8 coins meaning for 8/3 proportion of cake equals 8 coins.
      Therefore, if we count what person A contributes it comes to 1/3 portion after subtracting his share for food. It means he should get 1 coin.
      Person B is final score comes at 7/3 meaning she should get 7 coins.

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      Andy Kong

      25 May 2023

      Permalink
      Comment

      C is paying 8 coins for 8/3 cakes, of which 1/3 is contributed by A and 7/3 by B. To fairly share these coins, A should get 1 and B should get 7.

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      aston

      28 September 2023

      In reply to B is right by Andy Kong

      Permalink
      Comment

      so thats correcet answer

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