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Well, we’ve done a 3×3 logic puzzle, and a 4×4. I went crazy last week and did a 3×3x3. Today, I pull out all the stops with a 9×9. Hopefully, it works out well, and you won’t come after me with a 2×4.
Today’s Brain Game involves an intramural softball team from earlier this year. The nine players, Abe, Bob, Cal, Don, Eli, Fox, Gus, Hal, and Ike, pooled their money to buy the team jerseys for the upcoming season. To save money, they only purchased single-digit numbers for each jersey. So one of the players was #1, one was #2, and so on through #9. (There was no #0 jersey.)
Based on the following clues, can you determine which player wore which number jersey?
1. Hal’s jersey number is a prime number (and as a preemptive strike, 1 is not a prime number).
2. Fox’s number is equal to one-third of Bob’s number.
3. When written out, the digit on Cal’s jersey has the same number of letters as his name.
4. Don’s number is double Abe’s number, and Abe’s number is double Ike’s number.
5. Gus’ number is one less than Eli’s number, which was not odd.
Here’s the SOLUTION.
Comments (28)
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Another valid solution?
All the same except…
#5 – Gus
#6 – Eli
#7 – Hal
…since Hal only had to be a prime number and Gus and Eli separated by one, they can shift.
posted by Lindsey on 12-11-2008 at 3:44 am
Your answer is only one of three possible options. I’ve opted for the following:
1 – Ike
2 – Abe
3 – Fox
4 – Don
5 – Hal
6 – Cal
7 – Gus
8 – Eli
9 – Bob
My solution is based on the following: Bob is the only one who can be 9, there Fox is three. From here we have a conundrum. By listing the possible numbers each remaining player has as a possibility you find that only Cal and Ike can have the number 1. If Cal is 1, then Ike is 2, Abe is 4, Don is 8. That leaves two possible configurations for the remaining three players; Hal 5, Gus 6, Eli 7 OR Hal 7, Eli 6, Gus 5. Both of these are valid options with no solution. If on the other hand, we give Ike the 1, then Abe is 2, Don is 4. Eli must be 8 at this point making Gus 7, Cal 6, and Hal 5. This I believe is the only valid solution.
posted by Mark on 12-11-2008 at 4:12 am
What’s wrong with Ike(1), Abe(2), Fox(3), Don(4), Hal(5), Cal(6), Gus(7), Eli(8), Bob(9)?
posted by Zach on 12-11-2008 at 5:24 am
It seems like there is a clue missing allowing for a few correct answers because I ended up with the same lineup except I chose 7 as Hal’s prime number meaning Gus and Eli were batting 5th and 6th.
posted by Jake on 12-11-2008 at 5:37 am
I think there are many different solutions. For example, just put Fox/Ike/Bob/Abe in the 1-4 slots Cal at 6, Don at 8 and Hal at 9, then Gus and Eli are interchangeable at 5 and 7.
Also, technically, I don’t think this is a 9×9 puzzle but more like a 9×3…
posted by Chan on 12-11-2008 at 6:14 am
@Chan Hal can’t be 9 as 9 is not prime
What bout this though..
1-C
2-I
3-F
4-A
5-G
6-E
7-H
8-D
9-B
posted by Jason on 12-11-2008 at 6:59 am
I found 2 possible answers
a 2 4
b 9 9
c 6 1
d 4 8
e 8 6
f 3 3
g 7 5
h 5 7
I 1 2
posted by Dan on 12-11-2008 at 8:24 am
There is only one correct solution.
Ike-1,Abe-2,Fox-3,Don-4,Hal-5,
Cal-6,Gus-7,Eli-8,Bob-9
While other answers WORK, logic puzzles can only give one correct answer. There can’t be any interchanging answers as is the cases with Gus,Eli and Hal being interchangeable with the #’s 5,6 and 7.
posted by flintstone on 12-11-2008 at 8:28 am
i got the ike as 1 answer. i thought i had screwed up for a second.
posted by grant on 12-11-2008 at 8:30 am
Flintstone, I’m confused — I got the same solution as Sandy posted, but I also noticed what you posted works as well. It seems as this is a “flawed logic” puzzle as it has multiple answers…
posted by Aaron on 12-11-2008 at 8:34 am
Aaron,
In Logic puzzles, the answers to the clues have to be FORCED into being correct. So the only answer that uses the clues correctly in the one I and others posted. The other answers might work but you can interchange or just pick and choose your answer.
Ex. Gus, Eli, Hal at the numbers 5,6 and 7.
Since Hal has to be PRIME he can be 5 OR 7 (no definative answer) and the puzzle will still work.
In the correct answer, the clues FORCE the correct answers.
posted by flintstone on 12-11-2008 at 8:41 am
My box-by-box, and how I got to a fork in the road:
Clue 1: Eliminate H1, H4, H6, H8, H9 (prime numbers are 2, 3, 5, and 7)
Clue 2: Eliminate F4, F5, F6, F7, F8, F9, B1, B2, B4, B5, B7, B8 (If F>3, B>9, and if B mod 3 isn’t 0, F gets a fractional jersey number)
Clue 3: Eliminate C3, C4, C5, C7, C8, C9 (one, two and six are the only three-letter single-digit numbers)
Clue 4: Eliminate I3-9, A1, A3, A5-9, D1-3, D5-7, D9 (1-2-4 and 2-4-8 are the only options here)
Clue 5: Eliminate E9, E1, G9, and G8 (E isn’t 9, G can’t be 0, and G can’t be 10)
Having eliminated A9 (4), C9 (3), D9 (4), E9 (5), F9 (2), G9 (5), H9 (1) and I9 (4), we accept B9.
Having accepted B9, we eliminate B3 and B6. Furthermore, Clue 2 gives us F3 from B9.
With F3, we eliminate E3, G3, H3, F1 and F2.
Eliminating E3 and G3 allows us to eliminate G2 and E4 (5).
At this point, I’m out of things I can do. Clue 1, I have Hal as 2, 5 or 7. Clue 2, I’ve established Bob is 9 and Fox is 3. Clue 3, I have Cal as O-N-E, T-W-O or S-I-X. Clue 4, I can go 1-2-4 or 2-4-8 with I-A-D. Clue 5, I have 5 scenarios where (G = E-1): G is 1, 4, 5, 6, or 7.
I’m not sure how Mark eliminated G1, but he and I are at the same point: guessing. Using Clue 4 to assign I-A-D to 1-2-4 gives one solution, as he posted. Using 2-4-8 leaves Cal at 1 and the option of Sandy’s solution or Lindsey’s.
Somebody who’s sure about their solution (Flintstone or someone else), please show me where I went wrong, what I forgot, or how to resolve an ambiguity?
posted by Danno on 12-11-2008 at 9:17 am
I have a feeling Sandy is feverishly working to fix it so only one solution fits. Or perhaps watching a Harry Potter movie; because, really, how can you not love Harry Potter?
posted by Chris on 12-11-2008 at 9:51 am
I found three valid sets of answers.
1 – I C C
2 – A I I
3 – F F F
4 – D A A
5 – H H G
6 – C G E
7 – G E H
8 – E D D
9 – B B B
posted by KJ on 12-11-2008 at 10:02 am
No, not fixing, but trying to recreate my answer from last night. Almost done!
posted by Sandy on 12-11-2008 at 10:06 am
I need to find a better way to document myself when I come up with these…
This morning (with the time I had) I was able to get down to the Eli/Gus/Hal mix, but not beyond that. If I change the last clue to say that Eli’s number was not ODD (instead of just that it was “not nine”) it works. But I did get my “correct answer” three times in a row when I worked out the clues last night…
Here are my notes from this morning:
Hal’s jersey number is prime, which eliminates H1, H4, H6, H8 and H9.
Fox’s number is 1/3rd Bob’s number. The only perfect thirds are 9/3, 6/2 and 3/1, so Fox’s number is either 1, 2, or 3, and Bob’s number is either 3, 6, or 9. All other numbers for Fox & Bob are eliminated.
Cal’s jersey cannot be 3, 4, 5, 7, 8, or 9.
Don/Abe/Ike must be either 8/4/2 or 4/2/1. No other combinations work.
At this point, I named Ike=1 as “A” and Ike = 2 as “B” then distributed A and B through the grid in Don & Abe’s spots.
Since the #2 jersey must belong to Abe or Ike (only A and B are possible), no one else can have the #2 jersey. Same with the #4 jersey between Abe and Don.
Eli’s not #9 and neither is Gus (he’s one less), so Bob must be #9.
Since Gus’ number is one less than Eli, Gus can’t be #1, #3, or #8.
Then, because Eli’s number is one more than Gus’, Eli can’t be #1, #3, or #5.
Going back through our clues, Fox’s number is 1/3 Bob’s, and we know Bob is #9, so Fox is #3.
Hal has to have either #5 or #7. If he has #5, Gus must be #6 or #7. If he has #7, Gus must be #5 an d Eli #6 bec ause there’s no other choice. Either way, #6 will be either Gus or Eli, so all other choices for #6 are eliminated.
With Cal eliminated for #6, we now know he is #1.
Now we know that our “B” option above is the correct one, with Ike #2, Abe #4, and Don #8. Several others fill in at this point.
Now… we still know that Gus’ number is one less than Eli’s, so Gus can no longer be #7, he has to be either #5 or #6.
posted by Sandy on 12-11-2008 at 10:24 am
really not that hard….once you start with clue number 4…..just about all else fall in place.
couldn’t have taken more than 2 minutes.
posted by olal on 12-11-2008 at 10:53 am
Am I missing something? How can Eli be 7 if he is NOT odd? Shouldn’t it be 5 – Gus, 6 – Eli and 7 – Hal? Everything else I got was the same.
posted by Kim on 12-11-2008 at 11:25 am
Agree with Kim, after changing the last clue to say that Eli is not odd, you still made Eli an odd number in your answer.
posted by KLB on 12-11-2008 at 11:32 am
The sad thing is that I googled odd numbers to make sure I wasn’t having a blond moment =)
posted by Kim on 12-11-2008 at 11:34 am
To give:
1 – Ike
2 – Abe
3 – Fox
4 – Don
5 – Hal
6 – Cal
7 – Gus
8 – Eli
9 – Bob
posted by KLB on 12-11-2008 at 11:36 am
Danno,
The point where you are is KIND of like guessing. It is like guessing in a Sudoku puzzle. You have one clue (clue 4) that choosing either one gives you a 50% chance of being correct. So let’s choose the INCORRECT one (option 2,4 and 8)giving us D8,A4,I2 from clue4 and B9,F3.
So that leaves us with C,E,G,H
and #’s 1,5,6,7.
Cal can only be O-N-E or S-I-X
but we can eiminate 6 because then we wouldn’t have 2 consecutive #’s for clue 5.(Gus and Eli are consecutive)
So now we have D8,A4,I2,B9,F3,C1
leaving Hal to be either 5 or 7(only primes left) and then Gus and Eli can be either E6-G5 or E7-G6, both of these options work but you have to choose either 5 or 7. So since this option doesn’t FORCE and answer THEN YOU HAVE TO ELIMINATE D8,A4,I2 AS A POSSIBILITY LEAVING ONLY D4,A2,I1. This will give you the correct answer.
posted by flintstone on 12-11-2008 at 11:44 am
flintstone, I don’t see why the answer must be forced. If two options fit all the clues, both options are correct. After all, if you tested this in the real world, Ike might be confused to find that he couldn’t be #2. Good clues should force one answer, but forcing means that only one answer fits all the clues. After all, in your example you only eliminate the one because in your logical process you chose to do certain steps first; otherwise another answer would force.
The only ones that are forced are Fox at #3 and Bob at #9. With the others you have to pick one or the other; there are still multiple solutions that fit all the clues.
I still had fun with it, Sandy, so keep ‘em coming.
posted by M on 12-11-2008 at 12:31 pm
I *still* have 2 answers… the one given by Sandy and the one given by Mark in comment #2…. both fit all the clues just fine.
I agree with M though, keep these coming. I loved the 3×3x3 the most!
posted by Amanda on 12-11-2008 at 4:03 pm
Sandy I believe your logic on this response is flawed:
“Hal has to have either #5 or #7. If he has #5, Gus must be #6 or #7. If he has #7, Gus must be #5 an d Eli #6 bec ause there’s no other choice. Either way, #6 will be either Gus or Eli, so all other choices for #6 are eliminated.”
I agree with M, in that the only forced choices at Fox and Bob. The others are limited to 2 choices. Either one you pick follows the rules of the puzzle. Leaving two possible answers as listed below:
(Sandy’s Conclusion)
1. Cal
2. Ike
3. Fox
4. Abe
5. Gus
6. Eli
7. Hal
8. Don
9. Bob
(Alternate Conclusion)
1. Ike
2. Abe
3. Fox
4. Don
5. Hal
6. Cal
7. Gus
8. Eli
9. Bob
Am I missing something, I have run through this several times, and always come down to these two possibilities. Its a slow day at work, so thank you for giving me something to do.
posted by Vikter on 12-11-2008 at 5:11 pm
flintstone is talking nonsense. Consider this:
First read his explanation as it applies to the original puzzle (Eli is not 9). He says if he chooses Ike as 2 he reaches a point where Hal, Gus, and Eli must wear some combination of 5,6,7. Therefore that cannot be the solution, so the only solution is for Ike to be 1, etc.
Now look at the new puzzle (Eli is even). If he chooses Ike as 2, the Hal-Gus-Eli conflict is resolved and Eli must be 6. So this then becomes a valid answer (according to flintstone’s explanation). However the other solution (with Ike as 1) is still valid. That means that despite making the solutions more restrictive, we create additional solutions.
Just change the text from “Here’s the solution” to “Here’s A solution” and be done with it.
posted by Zach on 12-11-2008 at 7:23 pm
Thanks, folks… I appreciate your continued patience as I learn how to properly compose the more complicated logic puzzles. I’ll get there, I promise!
posted by Sandy on 12-11-2008 at 8:40 pm
uhhh, I’m going by the definition of what a logic puzzle is.
-=Merriam-Webster def. Logic: something that forces a decision apart from or in opposition to reason. =-
A logic puzzle answer has to be FORCED.
So in the ORIGINAL version of the puzzle there was ONE correct answer.
IN THE NEW VERSION there might be 2 answers, but as long as they are FORCED they are correct.
Take it easy people! I’m just giving some hints.
posted by flintstone on 12-12-2008 at 8:21 am