Loading...
For a particular custom basketball game, a player receives a personal warning upon accumulating at least 3 fouls within any 12 minute quarter and complete ejection from the court upon accumulating 5 such fouls at any time during the 48 minute game. For any single 48 minute game, missing between 2 minutes and 4 minutes of playtime counts as one-third of an absence, missing between 4 minutes and 10 minutes of playtime counts as half an absence, and missing more than 10 minutes counts as a full absence. However, a basketball player may postpone playtime to make up for up to 3 minutes of unexcused absence at another time.
The table contains descriptions of the unexcused absences of 5 players of a particular custom basketball game. Assume that in each case the basketball player had no other unexcused absences and made up no other time. In the table, select a description of a basketball player who qualified for a personal warning but not a complete ejection, and select a description of a basketball player who qualified for a complete ejection. Make only two selections, one in each column.
Fouled once in the first quarter, none in the second quarter, twice in the third quarter, and once in the fourth quarter
Fouled none in first quarter, none in the second quarter, twice in the third quarter, and twice in the fourth qaurter
Fouled none in the first quarter, none in the second quarter, none in the third quarter, and four times in the fourth quarter
Fouled twice in the first quarter, once in the second quarter, once in the third quarter, and none in the fourth quarter
Fouled once in the first quarter, once in the second quarter, once in the third quarter, and twice in the fourth quarter
We have two key thresholds:
Let's create a table showing each player's fouls:
| Player | Q1 | Q2 | Q3 | Q4 | Total | Warning? | Ejection? |
| 1 | 1 | 0 | 2 | 1 | 4 | ? | ? |
| 2 | 0 | 0 | 2 | 2 | 4 | ? | ? |
| 3 | 0 | 0 | 0 | 4 | 4 | ? | ? |
| 4 | 2 | 1 | 1 | 0 | 4 | ? | ? |
| 5 | 1 | 1 | 1 | 2 | 5 | ? | ? |
We need to find:
Player 1:
Player 2:
Player 3:
Player 4:
Player 5:
| Player | Q1 | Q2 | Q3 | Q4 | Total | Warning? | Ejection? |
| 1 | 1 | 0 | 2 | 1 | 4 | No | No |
| 2 | 0 | 0 | 2 | 2 | 4 | No | No |
| 3 | 0 | 0 | 0 | 4 | 4 | Yes | No |
| 4 | 2 | 1 | 1 | 0 | 4 | No | No |
| 5 | 1 | 1 | 1 | 2 | 5 | No | Yes |
Statement 1 (Personal warning): Player 3 - "Fouled none in the first quarter, none in the second quarter, none in the third quarter, and four times in the fourth quarter"
Statement 2 (Complete ejection): Player 5 - "Fouled once in the first quarter, once in the second quarter, once in the third quarter, and twice in the fourth quarter"
These selections satisfy our requirements perfectly: