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## Slam Dunk

 Category: Logic-Grid Submitted By: cnmne Fun: (2.64) Difficulty: (3.19)

The hotly-contested basketball game had just ended. Coach Shortfuse, enraged by what he considered poor officiating, grabbed the stat sheets and fed them into a paper shredder. Fortunately, the officials remembered several facts about the scoring. With this information, determine: each starter's first and last name, his position, his jersey number, and points scored.

First Names: Allen, Jason, Kevin, Shaquille, Tim
Last Names: Duncan, Garnett, Iverson, Kidd, O'Neal
Position: Center, Power Forward, Small Forward, Shooting Guard, Point Guard
Jersey Numbers: #12, #15, #23, #34, #44
Points Scored: 24, 22, 20, 11, 10

1) In addition to the five starters, three bench players also scored. One of the bench players was the fourth-leading scorer; the other two each scored less than 10 points each. All scoring players scored a different amount of points.
2) Kevin scored exactly one-fifth of the total team points.
3) The center scored more points than Allen, who scored more than #34.
4) #15 scored more points than Duncan, who scored more than Shaquille.
5) Garnett scored more points than the power forward, who scored more than #12.
6) Tim scored more points than O'Neal, who scored more than the shooting guard.
7) One of the forwards has "K" for an initial.
8) One of the guards has "K" for an initial.
9) The players that have a vowel for an initial wear jerseys with an odd number.
10) Iverson scored twice as many points as one of the bench players.
11) Allen scored 18 more points than one of the bench players.
12) Only one starter scored more points than his jersey number.
13) Neither forward wears an odd number.

Much of the grid can be filled using the normal process of elimination. An explanation for determining the bench scores and team score is provided.

The five starters scored a total of 87 (24 + 22 + 20 + 11 + 10) points. From clue 1, three bench players scored points in the following ranges: 1 through 8, 2 through 9, 12 through 19. This means that the team scored anywhere from 102 (87 + 12 + 2 + 1) to 123 (87 + 19 + 9 + 8) points. From clue 2, the team point total must be a multiple of 5. Kevin scored either 22 (team score = 110) or 24 (team score = 120). From clue 10, Iverson scored either 10 or 24 (11 can not be twice any integer, 20 or 22 would have been twice a starter's score). This means that a bench player scored either 5 or 12. From clue 11, Allen scored 20, 22, or 24 (10 or 11 would have had a bench player scoring negative points). This means that a bench player scored 2, 4, or 6. Since the bench player tied to Allen had a different possible score than the bench player tied to Iverson, Allen can not be Iverson. This leaves the following possible bench scoring combinations: 2, 5, 16; 2, 12, 9; 4, 5, 14; 4, 12, 7; 6, 5, 12; 6, 12, 5. With the 87 points scored by the starters, all combinations produce a team score of 110. The team score could not have been 120, since that would require one of the bench players to score more than 19 points, or require two bench players to score more than 9 points (both violating clue 1).

Allen O'Neal, point guard, #23, 20 points
Jason Duncan, power forward, #34, 11 points
Kevin Garnett, small forward, #44, 22 points
Shaquille Kidd, shooting guard, #12, 10 points
Tim Iverson, center, #15, 24 points