ONLY GENIUSES CAN SOLVE THIS! | Saurabh sir | Olympiad Preparation #maths #olympiad

Added: 2026-05-31

[00:00:01]fully empty, right? Nobody is there.

[00:00:04]Every minute either one person enter or three people leave the room.

[00:00:10]After exactly 2025 minutes, could the room contain exactly 203 people? This is the question.

[00:00:20]See.

[00:00:21]What is the approach? What could be the approach for this? Right? So, obviously, we have to go for 2025 minutes, right? So, we can start with first minute, second minute, third minute, and fourth minute. Just we have to see exactly what's going on.

[00:00:40]Right?

[00:00:41]So, this is the tree diagram of this.

[00:00:45]First minute, what is happening?

[00:00:47]One people or one person can enter the room, but we don't have three people, so we can't take out three person from the room. So, only one person is there. So, obviously, we have to start with plus one.

[00:01:02]What is happening in second minute?

[00:01:05]We can add a person, but again, we don't have three or more than three person, so we have we can't take out minus three from this. So, this is plus two.

[00:01:16]For third minute, again, we have to add one more, so we are getting three.

[00:01:21]And Now, la last is for fourth minute, we can see this key again, we are adding plus one.

[00:01:30]And obviously, minus three. Right? If we'll take out minus three, this will be zero. If we'll take out giving one, so this will be four.

[00:01:43]Right?

[00:01:44]So, can we see this key like in the fourth minute, either this is zero or four?

[00:01:51]Right? And this will be happening in every four minute, right? So, we can say this keep this number is coming as either zero or multiple of four.

[00:02:03]Means every four minute if we'll take at model four, so this will give you always the number zero.

[00:02:12]Right? So, from this we can frame out, right? Key every minute either one person can enter or minus three can go out from the room. So, one and minus three is the number that's going with the model four.

[00:02:30]Now, it's 2025 minutes and second is 203 people.

[00:02:39]2029 at 25 minutes, if we'll divide this by four, we're getting the remainder one.

[00:02:46]203 people when we are dividing this by four, we are getting three. Since the number one and three both are not equal, right? So, we can say key obviously this is not possible in this case.