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.

## Comments

Sort by:

TopNewestWell 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

```

```

Somebody also think.

ARYΔ – Arya Samanta · 2 years, 2 months ago

Log in to reply

– Calvin Lin Staff · 2 years, 2 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.Log in to reply