In a knockout mixed martial arts tournament, the winner of each round progresses to the next round until there are only two players left.

The diagram shows the draw for the final, semi-final and quarter final rounds.

a

Complete the table of values for the total number of players, $p$`p`, that the competition can accommodate given a number of rounds $r$`r`.

Number of Rounds ($r$r) |
$3$3 | $4$4 | $5$5 | $6$6 |
---|---|---|---|---|

Number of players ($p$p) |
$8$8 | $\editable{}$ | $\editable{}$ | $\editable{}$ |

b

Suppose that the mixed martial arts tournament organisers want to make sure that each round of the tournament has every spot filled.

For what values of $p$`p` can a tournament be formed?

Any multiple of $4$4.

A

Any multiple of $2$2.

B

Any power of $2$2.

C

Any even number.

D

Any multiple of $4$4.

A

Any multiple of $2$2.

B

Any power of $2$2.

C

Any even number.

D

c

Plot the points from the table of values on the number plane.

Loading Graph...

d

What is the equation relating $r$`r` and $p$`p`?

Give your answer in the form $p=\editable{}$`p`=.

e

The organisers of a tournament can fit in $9$9 rounds of play.

How many players can they accept into the tournament?

Easy

Approx 6 minutes

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