快猫短视频

#128 Tournament headache

Four hungover footballing mathematicians groaned in unison. 鈥淎nyone remember who won yesterday鈥檚 tournament between our four teams?鈥� asked Ranko, the Red Star Belgradient goalkeeper. Ignacio, the Integer Milan striker, raised his hand feebly. 鈥淚 remember that we each played each other once. Three points for a win. One for a draw. And all of the scorelines were different.鈥�

Tom, the Tottingup Hotspur defender, opened one eye. 鈥淎re 1-0 and 0-1 different or the same?鈥� 鈥淭hey鈥檙e the same, obviously!鈥� said Patrick, of PSV Eigenvector, adding: 鈥淚 remember that every team scored a different number of goals in each of their games.鈥�

鈥淏ut never more than two!鈥� said Ranko. 鈥淎nd I know my team didn鈥檛 concede a goal.鈥� Patrick pulled a silver medal out of his pocket. 鈥淎nd we must have finished second,鈥� he deduced.

鈥淚 know which game ended 2-2!鈥� said all four at once.

Which was it?

#127 Brahms and Liszt

Solution

It is possible to construct jigsaw-like pieces for the conditions and then see the possible ways they can fit together. The notion that only one item is correctly positioned gives the following unique solution:

First name  Surname  Composer

1 Claudio  Grump  Liszt

2 Agnes  Iddyhat  Khachaturian

3 Edgar  Hobble  Mozart

4 Dolores  Jabber  Schubert

5 Bjorn  Flop  Prokofiev