Today is my Birthday! I wil be cutting my own birthday cake and share equally to 11 of my friends.Assuming that I do straight cuts and there is no topping (I don't have money for topping :/) on a non-flat round cake, what is the minumum cuts needed for me to cut equally the cake for myself and friends?
Note:No, its not "0" this time! It's a legitminate answer!
First you draw $2$ parallel lines to divide the cake in 3 parts, then you draw a perpendicular line, getting 6 equal pieces. At the end, you make a longitudinal cut to split all the pieces, getting 12 parts (one for you and 11 for friends).
See this picture:
Another equivalent solution, perhaps simpler (and symmetrical), is this:
You need 12 pieces. You said you wanted to share equally to 11 of your friends, sharing implies yourself. Note that nothing implies needing to eat the whole cake, however the fewest amounts of cuts will have you eating the whole cake. The answer would be 6 cuts, or if you are really awesome at gauging pieces (since its a non-flat cake), you could cut the cake in half vertically and then make 3 cuts to divide the halves into 6 pieces each. But you'd have to be a walking computer to do that
You need 4 cuts are needed because you need 12 pieces (11 friends and you)
1- cut the cake in half vertically (you have now 2 pieces)
2- cut each half in third vertically (you have now 6 pieces)
3- cut the cake in half horizontally (you have now 12 pieces)