MHB Sorting $8$ Players in $24$ Hours: Is it Possible?

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The discussion revolves around sorting eight players based on their performance in a series of games conducted over a 24-hour period. Each game lasts one hour, and the players are ranked through a series of matchups. The proposed method involves organizing the players into matches to determine their rankings step by step. The calculations indicate that the best player, P1, was identified after 7 hours, followed by P2 in 3 hours, P3 in 2 hours, P4 and P5 in 1 hour, and P6 in 2 hours. Players P7 and P8 were sorted last in 1 hour. The total time taken to sort all players is calculated to be 16 hours. The participant questions whether this sorting method resembles an application of Mergesort, suggesting a connection between the game structure and sorting algorithms.
mathmari
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Hey! :o

We have $8$ players and we want to sort them in $24$ hours.
There is one stadium. Each game lasts one hour.
In how many hours can we sort them?? (Wondering)

I thought that we could it as followed:

$$\boxed{P1} \ \boxed{P2} \ \boxed{P3} \ \boxed{P4} \ \boxed{P5} \ \boxed{P6} \ \boxed{P7} \ \boxed{P8} \\ \ \ \ \ \boxed{P1} \ \ \ \ \ \ \ \ \ \boxed{P3} \ \ \ \ \ \ \ \ \boxed{P5} \ \ \ \ \ \ \ \ \ \ \ \boxed{P7} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{P1} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{P5} \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{P1}$$

So, the best player is $P1$.
These games took place in $7$ hours.

We know that $P5$ is the best player among the players $P5$, $P6$, $P7$ and $P8$.

$$\boxed{P2} \ \boxed{P3} \ \boxed{P4} \ \boxed{P5}\\ \ \ \ \ \ \ \ \boxed{P2} \ \ \ \boxed{P5} \\ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{P2}$$

So, the second best player is $P2$.
These games took place in $3$ hours.

$$\boxed{P3} \ \boxed{P4} \ \boxed{P5}\\ \ \ \ \ \ \boxed{P3}\ \ \ \ \boxed{P5} \\ \ \ \ \ \ \ \ \ \ \ \ \boxed{P3}$$

So, the third best player is $P3$.
These games took place in $2$ hours.

$$\boxed{P4} \ \boxed{P5}\\ \ \ \ \ \boxed{P4}$$

So, the $4^{th}$ best player is $P4$ and the $5^{th}$ best player is $P5$.
This game took place in $1$ hour.

$$\boxed{P6} \ \boxed{P7} \ \boxed{P8}\\ \ \ \ \ \ \boxed{P6}\ \ \ \ \boxed{P8} \\ \ \ \ \ \ \ \ \ \ \ \ \boxed{P6}$$

So, the $6^{th}$ best player is $P6$.
These games took place in $2$ hours.

$$\boxed{P7} \ \boxed{P8}\\ \ \ \ \ \boxed{P7}$$

So, the $7^{th}$ best player is $P7$ and $8^{th}$ best player is $P8$.
This game took place in $1$ hour.

Therefore, we sorted the players $P1 \geq P2 \geq P3 \geq P4 \geq P5 \geq P6 \geq P7 \geq P8$ in $7+3+2+1+2+1=16$ hours.

Is it correct?? (Wondering)
 
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Is it maybe an application of Mergesort?? (Wondering)
 
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