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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.

Note by Eddie The Head
2 years, 11 months 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 Arya Samanta · 2 years, 10 months ago

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@Arya Samanta 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. Calvin Lin Staff · 2 years, 10 months ago

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