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.

#Combinatorics #RecurrenceRelations #Recursion

Easy Math Editor

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Comments

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 - 6 years, 7 months 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.

Calvin Lin Staff - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$