Question

If 5 colors are used to paint 26 door prove that at least 6 doors will have same color

Answer 1

Please mark as the brainliest..if any explanation is needed please tell

Answer 2

Pigeonhole concept

By extended Pigeonhole principle atleast $[|\frac{n-1}{m}|]+1$, pigeons will occupy one pigeon hole.

According to question,

here $n = 26,$

$m= 5$

and $m < n \ \ i.e. \ 5 < 26$

hence,  $[|\frac{26-1}{5}|]+1=6$

Hence, it is proved that atleast 6 doors will have same color if 5 colors are used to paint 26 doors.

Note:

Extended pigeonhole principle states that if n pigeons are assigned for n holes then, then one of the pigeonholes must contain at least $[(n-1)/m]+1$ pigeons. Here number of pigeons is much more than that of holes.