Problem of the Month - February 2025

In hockey, teams play three 20 minute periods.  At the end of a hockey game, Team A had 4 goals and Team B had 2 goals.  How many different Team A to Team B scores were possible at the end of the first period?   

 

The possible scores were: 

0-0,

0-1, 

0-2, 

1-0, 

1-1, 

1-2, 

2-0, 

2-1, 

2-2, 

3-0, 

3-1, 

3-2, 

4-0, 

4-1, and 

4-2.  

 

So there were 15 possible scores.  How many scores would be possible at the end of the first period if the score at the end was Team A 5 and Team B 4?  

Department