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# Say cheese!

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How many regions can you obtain from a single thick piece of cheese by making five straight cuts?(The cheese must stay in original position while you do all the cutting and each slice must correspond to a plane in 3D).Find a recurrence relation for $$P_n$$,the maximum number of three dimensional regions that can be defined by $$n$$ different planes.

3 years, 1 month ago

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Well I obtain 18 pieces cut 2 slices with a plane and other 2 with another plane and the last one with the last plane. But I am still thinking of a recurrence relation for $$P_n$$

Starting with



 $$1 \Rightarrow 2$$ $$2 \Rightarrow 4$$ $$3 \Rightarrow 8$$ $$4 \Rightarrow 12$$ $$5\Rightarrow 18$$ $$6 \Rightarrow 27$$



Somebody also think.

ARYΔ

- 3 years, 1 month ago

Hm. I feel like 4 cuts should give us more than 12 pieces. The second to third cut already gives us 4 additional pieces, and I would expect that the third to fourth cut would give us more.

Staff - 3 years, 1 month ago