1. The elimination stage of the UAAP women's volleyball competition is played in two rounds where
each competing team plays against each of the other teams once in every round. How many games
are played in the elimination round if there are eight teams in a given season?
Understanding the Problem
The first step of Polya's Process is to understand the Problem. Some ways to tell if you really understand
what is being asked is to:
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State the problem in your own words.
Pinpoint exactly what is being asked.
Identify the unknowns.
Figure out what the problem tells you is important.
Identify any information that is irrelevant to the problem.
In the example, we can understand the problem by realizing that it’s a volleyball competition played two
rounds. Where it consist of 8 teams, plays against each other once in every round. So what we are trying
to figure out is to determine how many games are played in an elimination round in a given season.
Devise a Plan
Now that we understand the problem, we have to Devise a Plan to solve the problem. We could:
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Look for a pattern.
Review similar problems.
Make a table, diagram or chart.
Write an equation.
Use guessing and checking.
Work backwards.
Identify a sub-goal.
Answer:
Each of the 8 teams must play each of 7 teams twice.
So each team plays 14 games.
8 teams * 14 games = 112 games
But since there are two teams playing each game, there are really only half as many.
So half of 112 are required. = 56 games
Carry Out the Plan
The third step in the process is the next logical step: Carry Out the Plan. When you carry out the plan,
you should keep a record of your steps as you implement your strategy from step 2.
Answer:
To make that clearer.
Designate the teams as “A B C D E F G H” then we designate games as;
AB AC AD AE AF AG AH
BA BC BD BE BG BG BH
CA ...
DA...
EA ...
FA...
GA...
HA...
There are 8 * 7 = 56 games
And each team has played each other team twice, because
There is both a AB and a BA in the grid.
Look Back
The final step is to Look Back, which really means to check your work.
Answer: Looking back in the answer is process of assigning each team with a variable and multiplying
them to get the answer which is 56 games are played in a season.
2. Find the digit that is 50 places to the right of the decimal point in the decimal representation of the
rational number.