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Four teams take part in a week-long tournament in which every team plays every other team twice, and each team plays one game per day. The diagram below on the left shows the final scoreboard, part of which has broken off into four pieces, as shown on the diagram below on the right. These pieces are printed only on one side. A black circle indicates a victory and a white circle indicates a defeat. Which team wins the tournament?

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I have tried solving this problem as a puzzle, trying to fit in the pieces. I get the answer as D. ... Is 'D' the correct answer? ... Please advise.

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    $\begingroup$ Welcome to Puzzling.SE! Can you please provide the source of this puzzle? $\endgroup$
    – phenomist
    Commented Jun 17, 2018 at 5:43
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    $\begingroup$ (Ok, found it: 2007 Changchun Invitational World Youth Mathematics Intercity Competition Team Contest #6.) cauchy.math.nknu.edu.tw/math/country/pasttest/… $\endgroup$
    – phenomist
    Commented Jun 17, 2018 at 6:04

1 Answer 1

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There are two ways to dissect the remaining polyomino into the pieces displayed:
enter image description here
Since this is a tournament where every day each team plays one game, there are two games played each day, and hence two wins and two losses.
We can first fill out the bottom J-tetromino. The 2x3 box above it must have a differing number of wins represented in the two columns it sits in, so the J-tetromino must be the top left one, as those two columns have one win and one loss. This lets us also fill the other tetromino as all of its rotations are distinct. We are now at:
enter image description here
The U-pentomino also has distinct orientations, so we can place it too. Finally the 2x3 box's orientation is determined by the J-tetromino that we just placed:
enter image description here
In both scenarios, team C wins (in the upper one, it has 4 wins, and in the bottom it has 5 wins)

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  • $\begingroup$ Thank You very much @phenomist ... That was great help! ... $\endgroup$
    – Math Tise
    Commented Jun 17, 2018 at 17:55

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