Reasoning · Grade 4-2 Leagues and Tournaments
Problem
Each starting box allows a different game count.
In a knockout bracket you keep playing only while you keep winning, so counting the steps from a box up to the top tells you the most games that box can give.
4.OA.A.3Draw A DiagramWinning in 2 games puts Tyler in the leftmost box.
The one player who gets a free pass into the semifinal is the player in the leftmost box, and only a free pass lets the champion win the whole thing in just 2 games.
4.OA.A.3Eliminate PossibilitiesOnly the leftmost bottom box can give Tyler the number of games his clue demands, so that box is forced.
Each starting box sits at a definite depth in the bracket, so it offers one definite maximum number of games.
Every other box offers too few games, so all of them are crossed out and one candidate is left standing.
Mason takes one of the two rightmost boxes.
Mason is written one level up on the right, and the only way to get there is by winning the game between the two right-hand boxes.
3.OA.D.8Eliminate PossibilitiesOwen cannot take the other of those two.
Two people in the same pair of boxes are forced to meet, so 'they never played each other' means they cannot be paired.
4.OA.A.3Eliminate PossibilitiesOwen and Dylan fill the middle pair and Owen wins.
If a clue says one player beat another, the bracket has to give them a game together, and there is only one game Owen can possibly win.
4.OA.A.3Eliminate PossibilitiesThe last box is Grace.
With five names and five boxes, once four are placed the fifth has nowhere else to go.
3.OA.D.8Eliminate PossibilitiesThe four games match all three clues.
Writing out every game that was actually played is the fastest way to re-read all three clues at once and catch a mistake.
4.OA.A.3Make A Systematic ListIn a knockout bracket, where you start already decides how many games you can play — so 'how many games' is really a clue about where a name goes.