chose problem

I don't want to sound flip, but I'm having trouble understanding how you're wording this problem, and I get the feeling the beginning of it may be missing.

Are you asking how many people would have to be selected from an unknown, larger group of people in order to assure that at least 4 of them had the same birthday?

Or are you choosing 4 people born on the same day of the week?

you are right sorry for my english. problem is like yours.

It's a problem in that area of probability theory called combinatorics, and probably involves a calculation using binomial coefficients, but I am not energetic enough right now to re-learn the subject enough to do the calculation. This kind of stuff is often treated near the beginning of probability and statistics books. Combinatorics deals with questions like "How many different results can be obtained when k distinguishable objects are selected from a total of n?"

Logically (if we're talking about day of the week), it seems to me you'd have to pick 22. It is possible to have 21 people and have three of them have their birthday on Sunday, three on Monday, three on Tuesday, and so forth. But in that situation, the 22nd person chosen would have a birthday on the same day as three other people. So if you have 22 people in a room, at least four were born on the same day of the week.

Is it day of the week or day of the year?

If it's of the year the answer is 3*366+1 (because 366 possible dates, including Feb 29).

A more interesting question would be to ask how many people must be in a room to have a 50% chance that four have the same birthday. I believe for two to have the same birthday, the answer is 30, although it's been a long time since I've seen the calculation.

I agree, it is still unclear day of week or day of year. Your 2nd post eliminates finding 4 people born on July 5, 1904, or some other date. In any case the "at least" makes the answer infinity.
You might have 71 born on Sunday, 9 born on Monday, 77 born on Tuesday 65 born Wedensday, 23 born on Thursday 3 born on Friday, and 56 born on Saturday. The odds are very low of only 3 on Friday, but it could happen.
A different interpretation is: Only 4 people in the room, all of them born on Tuesday. A rare coincidence, but it could happen. That would be the least number in the room. Neil