Question

Kenny, Abby, and Ned got together for a round-robin pickleball tournament, where, as usual, the winner stays on after each game to play the person who sat out that game. At the end of their pickleball afternoon, Abby is exhausted, having played the last seven straight games. Kenny, who is less winded, tallies up the games played: Kenny played eight games Abby played 12 games Ned played 14 games Who won the fourth game against whom? Hint How many total games were played? (Become my friend...follow me=follow u back )

Answer 1

We have three players in a round-robin pickleball tournament, where -

• Kenny played 8 games
• Abby played 12 games
• Ned played 14 games

The first thing we need to do in find out the total games played. When we add up the total games played by Abby, Kenny and Ned respectively, we get -

$8 + 12 + 14 = 34$

However, a round-robin pickleball tournament is played with two participants in each match.

So, $\frac{34}{2} = 17$

Now, consider this. When we have three players in a round-robin pickleball tournament, we can infer that each player has played at least every other game. With 17 total games being played, each of the three players must have played at least eight games in the tournament. In the tally, we see Kenny played eight games. We can organise it as given in the diagram below.

There is one observation made from the table. If Kenny had won any of the 8 games he participated in, we would have seen two or more successive shaded regions. But, as seen from the table, Kenny must have lost in all the 8 games.

∴ Kenny lost in the fourth game as well.

Now, we need to find Kenny's opponent in the fourth games.

As evident from the question and the table,  Abby and Ned played against each other in every game that Kenny couldn't participate in, i.e. the unshaded squares. From the question, we know that Abby played in the last seven games successively.

∴ Abby played in match numbers 1, 3, 5, 7, 9, 11, 12, 13, 14, 15, 16, & 17.

Then, Ned must have played the rest of the games against Kenny. That means it was Ned who defeated Kenny in the fourth game.

Ans) (a) Ned defeated Kenny in the fourth game.

(b) A total of 17 games were played in the tournament.

Answer 2

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