Adam in the night in his room thinking about his possible strategies for the next match.
Adam: Between 1 and 100... Sure everyone would choose between 80 and 100, right? The chance of winning with a number lower than that is really low. The higher the stronger, so maybe should I go for 100? But wait, others surely think that too, then 99? What if others think this as well? Then 98 should do? Or 97? maybe 96? No way aghh- My logic breaks down! How should I decide on what I should do then?
...
Adam: Hmm... Now that I think about it, it sounds similar. Yeah! It sounds similar to
"The Unexpected Hanging Paradox.".
It's about a Judge and a culprit. The judge promises to the culprit that he will be hanged in the next weekdays of the next week, from Monday to Friday but there is a catch. The judge doesn't tell the culprit when he will be hanged, it will be a surprise.
So the culprit thinks that he cannot be hanged on Friday, because if he is still alive Thursday, then only Friday is left and it wouldn't be a surprise! But with this logic now Thursday is the last day, which means that if he is still alive until Wednesday night, then he can only be hanged Thursday, but then it's again not a surprise and this goes on. The conclusion: The culprit cannot be hanged. He is cool with his situation, thinking he cannot be killed but then they hang him Wednesday. He was surprised. Similar to this game, choosing 100? It's too obvious, 99? But surely others think the same, and this goes on. This logic is unusable. Especially that it has a flaw.
Adam: Huh. Then I really should just guess...? Whatever...
The next day...
Alarm goes off.
Adam: Hmm... It's already 9... dah why am I so tired? I didn't sleep too well...
Knock Knock
Adam: Gah, who could it be...
Adam opens the door.
Bandeer: Hey Adam.
Adam: What? Why are you here?
Bandeer: Oh, nothing. I just thought I would tell you that I will 94 in the first round!
Adam: Huh? Wait, why are you telling me that and- Hey! Where are you going?
Bandeer: I just wanted to tell you this bye!
Adam: What's with him? Whatever I should get ready for the game, it's just about an hour until we start.
The time flies away fast, only minutes to start. Everyone is in the main hall already... Someone seems like already have a plan
Csanad: ADAAAM! Good to see you my friend! I'm sorry for your loss!
Adam: Oh, my-. Are you talking about Greg?
Csanad: Yeah of course! So I heard what he said when he lost, so it seems like you and Oli are no longer teammates! How about we actually work together this time? I heard you want allies!
Adam: What?
Csanad: What "what"? You heard what I said! It sounds amazing isn't it? Oli doesn't want to see you anyway!
Adam: Y- yeah? Uhm... Sure...
Csanad: Don't be so shy! You will be awarded by Todor in the end! You just have to be useful! And trust me I have a plan that will make all of us useful in the next game so all of us will earn!
Adam: You really do?
Referee No.1: Welcome everyone! If everyone is here, which seems like it is the case, then we should just start the game! I hope all of you have your tablets ready and charged!
Round 1 starts NOW! 5 minutes until the end of the round!
Adam (Wait! Where is Oli? Hah? Oh! He's there...)
Oli from the other half of the main hall was already looking at Adam.
Oli: Tchh..
Adam: Oh...
Csanad: What's the problem Adam?
Adam: N- nothing... So uhm... Do you have a plan?
Csanad: Yeah, but for now we should all just be far away from Oli to not hear us of what we are planning. Also Todor told us all to not choose 100 so he can win with that.
Adam: Really? Todor told you to? Also, the players who are not here are not allies?
Csanad: Yeah, there are a few people who are just dumb, really. It would be free money.
Adam: So what will we do then?
Csanad: Just choose a number you would like that is not 100. It doesn't matter.
Adam: Alright... Then I will... (Hmm, Bandeer said he will choose 94, so I should go for something higher)
Players soon begin on the first round of guessing.
Referee: The first round of guessing ended! Let's see the results! I will show you the number and next to it the number of people who have guessed that number!
100 - 2
99 - 4
98 - 5
97 - 7
96 - 5
95 - 2
94 - 1
Referee: The highest unique guess in the first round is 94! (not factorial)
The first winner is Bandeer!
Bandeer: Kukuku! Thank you all! Thank you for the free win! You are all so easy to outsmart!
Adam: W- Wait! So that's why you said you will pick 94?
Bandeer: Hm? Oh it's you again, Adam. Yeah. So basically I did not just tell you that I will pick 94. I told it to everyone I could find before the match started. That's why you chose a higher number as well, right? You knew I picked 94, so if you pick the same as me or lower, then you have no chance at winning. So obviously, you will pick a higher number than 94, but there are not a lot of numbers out there that are higher than 95 but not more than 100, so of course every number will be picked more than just once.
Adam: Phew, I know you are smart, but now that I think about it, where is your usual monologue? Your explanation was always "Well I'm just lucky".
Bandeer: Kukuku! Yeah you right. I say that a lot.
Adam: Ah! Look over there!
Bandeer: Why, what's there?
Oli and Todor are standing and facing each other.
Todor: Oli, you were the other one picking 100, right?