knock-out competitions

this has some mathematical content (involving powers of 2 and general rules) but is mainly concerned with logical thinking

people do organise such competitions (sometimes badly) so it is a genuine task

students are asked to organise a competition for a number of teams (11 initially)

after some initial exploration and discussion about arranging the competition for 11 teams, suggest that there will only be byes in the first round from now onwards

different groups/pairs can be given various numbers of teams to explore 

a ppt of team names for various numbers is here

the resources for ‘teams’ could be printed off for pairs to work on

as an extension, high attaining students could be asked for a more detailed competition:

e.g. for 14 players where they are seeded

arrange for the seeds to be distributed so that there is fair competition with e.g.

‘good’ semi finals

e.g. seeds 1 and 2 do not come together too soon

lower seeds stand some kind of a chance (not too big a gap between them in the first round)

an actual competition, to consider:

how many teams took part?
how many byes were there in the first round?
how many rounds were there?
how many games altogether?











a rule for the number of byes can be found by working towards the next biggest power of 2
the number of matches is obvious (since only one team/player wins, the rest have to be knocked out)