Before the World Cup began, the Argentine creator Valen Scarsini, known as El Scarso, launched an irresistible idea: to find the least-known footballer in the tournament and turn him into the protagonist.
The chosen player was Tim Payne, a defender from New Zealand. His case exploded on social media precisely because he started from almost nothing: he was not a hidden star, but the quiet name the internet decided to lift up.
This riddle imagines that search as a logic problem.
The Tim Payne Case
Riddle statement
In the days leading up to the World Cup, an Argentine content creator set out to find the least-known footballer in the tournament. He was not looking for a hidden star or a young prospect, but for exactly the opposite: the player with the fewest followers, the most discreet name of all.
Suppose he starts with a list of 32 players, but cannot see how many followers each one has. He can only make one kind of check: compare two profiles and learn which one has fewer followers.
After making the necessary comparisons, he identifies the least-followed player on the list: Tim Payne. He also manages to identify, with complete certainty, the second least-followed player.
What is the minimum number of comparisons he needed to guarantee the identification of both?
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Solution
Answer: it takes 35 comparisons.
The efficient method is to organize a tournament among the 32 players.
In each matchup, two profiles are compared, and the player with fewer followers advances.
Each comparison eliminates one player from being the least-followed: if he loses the matchup, we have already seen someone with fewer followers than him.
To get a single winner from 32 players, we need:
comparisons.
That winner is the least-followed player on the list. In this story, it is Tim Payne.
Now we still need the second least-followed player.
The key is that the runner-up can only be among the players who lost directly to Tim Payne.
If a player lost to someone other than Tim Payne, then at least two players are ahead of him:
- the player who beat him;
- Tim Payne.
So he cannot be second.
Since the tournament has 32 players, the winner plays 5 rounds:
Tim Payne won 5 matchups, so there are 5 candidates for second place: the five players who lost directly to him.
To find the least-followed among those 5 candidates, we need:
more comparisons.
In total:
So the minimum is 35 comparisons.
The tournament does more than find the least-followed player. It also marks the only place where the second least-followed player can be hiding.