A psychic calls everyone on a list of $275$ sports bettors with tips about who will win the "hard-to-predict" games in the first round of the NCAA "March Madness'' tournament.
This tournament has $4$ groups of $16$ teams, ranked $1−16$ within each group.
Teams ranked $(8,9)$ and teams ranked $(7,10)$ in each group play each other - these are the hard-to-predict games.
At the end of the call, the psychic gives their Venmo and tells the bettor to send money for future predictions. Explain how the psychic can correctly predict all hard-to-predict games for someone but would have trouble predicting any more games.
I am not getting any clue how to approach this problem.
Any hints will be of great help.
There are 8 hard to predict games with 2 in each group. So there are $2^8=256$ possible win-loss outcomes [I believe that in a tie as many overtimes as needed for one team to win are played].
This means that there is a slack of $275-256=19$ bettors left over.
But even predicting another game requires predicting 9 total games which have $2^9=512$ possible outcomes.