How many crates must be selected to be certain that at least 3 crates contain exactly the same number of oranges?

Question

Each crate contains at least 230 oranges and at most

235 oranges. How many crates must be selected to be certain that at least 3 crates contain

exactly the same number of oranges?

Answer 1

230<c<235

it's the same as 1,2,3,4,5,6 oranges per crate

pick crates until you get 3 with the same number of oranges

take the easiest problem 1 crate with 1 orange,

it takes 3 selections to get a guaranteed 3 crates of the same number of oranges

take the next easiest problem, with just 2 crates, one with 1 orange and a 2nd with 2 oranges.

You need to select at least 5 crates to get at least 3 crates with either 3 crates with 1 orange each or 3 crates with 2 oranges each.

up the oranges to 1&2&3

it now goes from 3 to 5 to 7

try crates with 1,2,3, & 4

now it's 9 minimum

1 through 5, 11

1 through 6, 13

that's 3,5,7,9,11,13 for 1,2,3,4,5,6 crates

13 random selections will lead to a certain 3 crates with the same number of oranges