Pigeon hole problem unknown pigeons numbers

Question

I am trying to solve an exercise but I am not sure if I handle it right.

let's suppose we have 40 letters of the alphabet. The 20 of those are with small letters and 20 are with capital.What are the minimum numbers of the letters that have a text with capital letters, so that the text to contain at least 10 same letters?

what I have tried: The 20 smaller letters can be ignored because we only want to learn about 20 capital letters.The text is in capital so we only care about 20.

Now I have lets call it a variable n.The variable n represents the pigeons(which is the text),the text is unknown the length it has.What we know is ,that we care about pigeonholes that are 20.We need to place the n into 20 so that we will take 10 at least.

what I think is $n/20$ =10 that means n= 20*10 =200. Am I right?

Answer 1

You have $20$ pigeonholes and want to know how many pigeons that you must have so that at least one of the pigeonholes has $10$ pigeons. If all $20$ pigeonholes have $9$ pigeons, you will have accommodated $180$ pigeons.

Then, the next (i.e. $181$-th) pigeon will have to cause one of the pigeonholes to have $10$ pigeons.