your task is to cut this pie (shown below) into seven equal parts.
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What equal means by is size and shape
you have only one knife of length equal to cakes diameter and a scale to measure W and D but nothing else
Edit : Also there should be nothing of cake that that is wasted/eaten
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2$\begingroup$ Can't we just cut it into 8 and eat 1? :) $\endgroup$ – Mark N May 27 '15 at 13:02
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2$\begingroup$ But how can you be sure? You just 'guess' something? $\endgroup$ – Mathias711 May 27 '15 at 13:47
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4$\begingroup$ So cutting into sevenths by eye in the traditional way would be a equally valid answer? $\endgroup$ – Bob May 27 '15 at 14:07
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1$\begingroup$ @Bob I +1ed your comment because this is a vague and overly broad question, but I think the idea is that you have a ruler but not a protractor. So, say W is 7cm, then you can make horizontal incisions at 1, 2, 3, 4, 5 and 6 cm heights using your ruler. But in order to cut slices of the right angle you would need something to help you measure 51.4°, and you don't have anything to do that with. $\endgroup$ – starsplusplus May 27 '15 at 15:57
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1$\begingroup$ It's gonna be much much easier to cut 7 conventional slices just using the eye to judge the angle, than it is to make 7 perfectly level horizontal slices through the whole cake. $\endgroup$ – dennisdeems May 27 '15 at 18:03
Silly solution:
You cut through the Height? (the W in the picture). So you end up with 7 slices with the same diameter as the whole cake, but just 1/7th of its height.
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$\begingroup$ +1 Answers are not silly....rather the way we think are :) $\endgroup$ – user2408578 May 27 '15 at 13:14
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2$\begingroup$ @user2408578 But what about the crust/icing. The top/bottom slice will get almost all of it!! $\endgroup$ – Mark N May 27 '15 at 13:18
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9$\begingroup$ How do you plan to measure the height of each slice? $\endgroup$ – Luke May 27 '15 at 13:55
It's not possible to cut a circle into 7 pieces using geometric methods: Is it possible to divide a circle into 7 equial pizza slices..., unless you allow Neusis construction; see Heptagon for details on constructing a Heptagon, which can be overlaid on the pie and used to guide the slicing.
The only good solution that avoids geometry is the height-based slicing, as suggested by Anon.
Place a quarter in the center of the pizza.
Arrange seven dimes around the quarter.
Insert seven toothpicks in the “V” between the dimes.
Use the tooth picks as a guide to slice the pizza to the perimeter.
All seven eaters may enjoy equal slices.
Eight easy steps:
- Make incision marks around the perimeter as for it being cut into 8.
- Then take one of the 8th pieces, and guessage it into 7 divisions.
- Then cut the first slice according to a Sixth+theSeventhOfTheSixth.
- Once cut down both sides to the centre, take it and lay it on top of the next slice you want to cut.
- Make a deep cut.
- Rinse and repeat until you've marked out the whole circle.
- Cut into seven.
- Send me money.