### Brain Teasers

# Slam Dunk

Logic-Grid
Logic Grid puzzles come with a handy interactive grid that will help you solve the puzzle based on the given clues.

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.

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.

### Answer

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

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## Comments

I dont think the points are the right numbers - the total is 87 which is not evenly divided by 5 an d one value is 10 but there are not 2 less than 10...

The 87 points were just for the starters. The bench players added to that: one was 4th, meaning he scored between 11 and 20, and 2 others were less than 10, all a different amount, so the total was between 101 and 123, thus Kevin had to be either 22 or 24 points.

A Very GOOD grid!! The off grid calculations that were necessary really made this one stand out.

This logic puzzle made absolutely no sense to me. And judging from one of the above comments, I'm not the only one. Perhaps you should have a hint attached?

It took me a long time to decide to include the bench players; when I did, I was able to click a couple more times, but to no avail: I lost! Too smart for me, but I enjoyed reading the answer!

Awesome logic grid! I had a lot of fun with this one.

I love this teaser! With all my hard work at solving it...I still ended up with the jersey numbers for #15 and #23 reversed. But what fun it was! Give me more!!

like what game are they playing, lol, starting with the first clue I was confused.

Lots of fun and very hard. I had to start over 3 times!!

very hard. I gave up. I don't know what a bench player is, so I was very confused the whole time.

Chaskey was right!!! it was too smart for me but good!!!!

Why scramble the players' names? If one is to solve this logically, knowing the names of the players helps. The scramble just adds to the confusion.

that waz so hard i almost gave up talked my self outou it and still got some wrong! great puzzle

the clues barely make sense how is anyone one able to solve this...i would have never figured out some of the clues if i hadn't read the comments...but who are these bench warmers? include them in your puzzle to make less confusing!!

This was way too hard and confusing i didnt like it at all and i love basketball and i know wat a bench warmer is it is someone who sits on the bench while the other people play Duh! any way i didn't like it

"The players that have a vowel for an initial wear jerseys with an odd number."

It doesn't specify first or last initial and there are 3 players with a vowel for an initial. I am going to assume you mean last name, but that is a big assumption...

I haven't given up yet... Just wanted to say that...

It doesn't specify first or last initial and there are 3 players with a vowel for an initial. I am going to assume you mean last name, but that is a big assumption...

I haven't given up yet... Just wanted to say that...

forgot to add:

and there are only 2 odd numbers...

and there are only 2 odd numbers...

The implication is that if there are three names that have a vowel as an initial (one first name and two last names), but only two odd numbers, then one of the players has both a first and last name with initial vowels.

After more than a dozen tries, i finally got it. That was really confusing, but well done.

Great teaser! Don't listen to the people saying that it's too hard or confusing, there are plenty of easy puzzles out there for them and not enough of these challenging ones.

Extermely tough teaser. I don't even know how many times I've tried this teaser and failed. Finally got it though. Great challenge.

I feel that there should be some sort of hint for those of us that love logic puzzles and do not love basketball - for I personally have no clue who would be the bench and who would be a starter. Did not care for this one - but that is not to say that this is not a good puzzle. I am sure it is, but just not for me.

Excellent puzzle. I appreciate that you provided the logic behind the solution.

You wrote that from clue #11, Allen scored 20, 22 or 24 points - but remember that from clue #3, the center scored more points than Allen; therefore, Allen scored either 20 or 22 points and the corresponding bench player scored 2 or 4 points.

That leaves 4, not 6, bench scoring combinations.

Also, it would have been clearer if clue #1 were written as "the other two scored less than 10 points EACH". I first read it assuming they scored less than 10 points total. Again, very nice puzzle!!!

You wrote that from clue #11, Allen scored 20, 22 or 24 points - but remember that from clue #3, the center scored more points than Allen; therefore, Allen scored either 20 or 22 points and the corresponding bench player scored 2 or 4 points.

That leaves 4, not 6, bench scoring combinations.

Also, it would have been clearer if clue #1 were written as "the other two scored less than 10 points EACH". I first read it assuming they scored less than 10 points total. Again, very nice puzzle!!!

Wow, I figured out the total score and the bench scores, but still managed to mess up my grid. Excellent job on this one!

Jan 15, 2009

Fantastic puzzle, cnmne! I like that I had to actually think and do some math to get the right answer.

Nice work. Love your puzzles!

Nice work. Love your puzzles!

Jul 04, 2009

I aslo finished the puzzle but got the #15 and #23 mixed up...

But if you go back over the clues the way it finished i cant find a problem...

So if you would be able to let me know why it is wrong and how you came to that conclusion...

But if you go back over the clues the way it finished i cant find a problem...

So if you would be able to let me know why it is wrong and how you came to that conclusion...

Wow is all I can say...It took me a few tries and a lot, A LOT of time to finally get this one. I am so glad to finally get this one done....But very, very good teaser...... I got to say this one was a very tough brain teaser but it can be done....Keep em coming....

I LOVED this logic-grid!!! Actually made you think, which is great..Plus you had some off-grid calculations, which made it more difficult-actually required work, but that's what made it a GREAT puzzle! So glad I did this one!

This was a great puzzle. I didn't find the bench players or scoring a problem. What i did find was that you could switch jersey numbers 23 and 15 and still have all the clues correct. Please help me if i overlooked something. I came down to those 2 unknowns and could not find the clues that would specify which one had which. Other than that this was one of the best.

Ok, I found it. I overlooked clue 12

Great puzzle!

Great puzzle!

Great puzzle! I enjoy the more difficult ones, and especially ones that require a little extra calculating. And, for the record, I know nothing about basketball and didn't find that a problem. It was apparent from clue one that there were 3 additional players who scored points. Who cares what they're called?

I have worked this puzzle at least 6 times and still can't get it. I've come so close but still no glory. I'll keep plugging away at it though...I will win this one. I will!

Great teaser. Making me think super hard and breaking out the math and reasoning skills. I love working your teasers.

Great teaser. Making me think super hard and breaking out the math and reasoning skills. I love working your teasers.

Wow, that was a toughie! I hit a brick wall so started to read the answer, then realised I had two bench players scoring over 10. Once I had that sorted, the rest fell into place - eventually! Definitely one of the best puzzles on this site; well done cnmne.

Thank you, thank you, thank you!!! GREAT teaser, I am so happy I found it, I think it's the best one I've run across. It required logic and the grid and a bit of puzzling to solve. Isn't that the point? LOL, well, you should be proud of your abilities, I'd love to be able to write a teaser like this! And for sharing - did I mention Thank you...

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