Difficult Logic Puzzle - Need Help
Long ago, on a quite summer night Bilbo and Frodo met Merry and Pippin in the Green Dragon for dinner. Not long after they sit down Bilbo starts to tell stories from his travel beyond the Shire. He talks about giant trolls that wanted to roast him as Rosie Cotton and Sam Wise Gamgee join them. Rosie thinks the stores all just Bilbo’s fantasy. They all order drinks and Bilbo continues his tales until late that night.
In the end they drank 1 pitcher, 4 Bottles, 5 pints, 6 humpens, and 8 tankards and 9 mugs. To pay their tap they needed to find out who drank what.
1. The “lager” beer was served in and drank from a “pitcher”.
2. “Sam” is always cautious in public and knows that he needs to pay $40.
3. The stout beer was neither served to the hobbit that had to pay $55 nor the one who drunk from the “tankards”.
4. Bilbo had to pay more than Pippin and less than the hobbit who drunk the hefeweizen.
5. Neither the hobbit who drunk from the “tankard” nor the hobbit who had to pay $50 was the one who drank the “Dark Ale”.
6. The six hobbits were “Pippin”, the one who drunk the pints and ones who drunk “Dark Ale”, “Pilsner”, “lager” and Hefeweizen”.
7. Everybody knew “Merry” loves “Pilsner”.
8. The hobbit who drunk from the “ tankards” paid 5 dollars more than the hobbit who drunk from the “bottle”.
9. By the time they had to pay, Frodo was still not finished with his larger.
10. “Merry” paid 10 dollars more than “Frodo”.
11. The customer who paid $40 was either “Sam” or the customer who drunk the “mugs”
12. The hobbit drinking porter did not drink form mugs or bottles, and was not Rosie.
Doesn't seem to have a unique answer to me.
Its a 4x6. Since the minimum amount mentioned is $40 and the maximum mentioned is $55, and there is a $5 delta mentioned, there should only be three possible ranges for the costs:
$40, 45, 50, 55, 60, 65
$35, 40, 45, 50, 55, 60
$30, 35, 40, 45, 50, 55
Creating the 4x6 grid and filling in the known fields and relative positions, without knowing the cost range doesn't appear to narrow the cost range choices.
So, arbitrarily choosing to start with the first one, $40 as the minimum, and then working the clues also doesn't seem to result in a unique solution, unless I've made a mistake I can't see.
I only worked through two possibilities, and didn't see any conflict, so would assume there are probably more than two solutions.
I'll post the two I came up with, and see if anyone wants to point out a clue that invalidates one or both solutions.
Ok, I see on second review (unfortunately after I posted), that the second "solution" fails clue #8.
I'm still not convinced that the first solution is unique though, since it was the result of arbitrarily starting with $40 and making some guesses along the way.
Since I'll be starting from scratch, if I decide to continue to disprove that the first solution is unique, I guess I would start the range at $35 (which would move Sam to the second row), to see if another solution seems to be valid, rather than take another shot at the $40 minimum.
p.s. Just ran through a possible $35 minimum scenario, and the first one seems to be a valid solution, and there could be others. I'm thinking this is not a good logic puzzle. Perhaps another pair of eyes can verify I didn't mess up again.
This is a Lord of the Rings geocache puzzle described at: http://www.geocaching.com/geocache/GC4BDYD_lotr-026
I had to make a few assumptions about the range and the increment for the A category just like Passel. I used a $40 minimum and a $5 increment. I assumed that the increments were constant across the range.
I got the following solution:
$40 - Bilbo - pint - porter
$45 - Frodo - pitcher - lager
$50 - Merry - tankard - Pilsner
$55 - Pippin - mug - stout
$60 - Rosie - bottle - hefeweizen
$65 - Sam - humpen - dark ale
This leads to these coordinates if I have interpreted the geocache instructions right: N 34 48.518 W 92 24.946. According to Certitude, these are not the correct coordinates. So at least you know one combination that doesn't work :).
You are correct on what this puzzle is from. I am a geocacher and have been stumped on this puzzle for a while. Several puzzlers make logic puzzles.
The variables as I saw them are:
Frodo, Pippin, Bilbo, Sam, Merry, Rosie
Pilsner, Larger, Hefewran, Dark Ale, Porter, Stout Beer
Pitchers, Bottles, Pints, Humpens, Tanlards, Mugs
40, 45, 50, 55, 60, 65
Think $40 was out base number and we need six number the only option seems to be 65 without duplicating a number.
I know the coordinates but wanted to figure out how to get them by solving the puzzle. There are several geocaches placed in this area. I knew the numbers I had to work with so using the process of elimination and a couple hours of work I found a likely spot. The numbers need to end up in the following order. 961 548
This is what I came up with but I have not been able to figure out the top two beverages. Who gets stout or dark ale?
9 mugs - $40 - Sam - Stout or Dark Ale
6 Humpens - $45 - Rosie - Stout or Dark Ale
1 Pitcher - $50 - Frodo - Larger
5 Pints - $55 - Pippin - Porter
4 Bottles - $60 - Merry - Pilsner
8 Tankards - $65 - Bilbo - Hefeweizen
I must have read those 12 sentences 100 times.
I didn't go through all the clues, but your solution fails by the time you get to clue #4
Bilbo had to pay less than the hobbit that drank Hefeweizen, and you have Bilbo both paying the most and drinking Hefeweizen, which are two things Bilbo can't be according to clue #4.
I was going to assume the numbers you gave were correct, 961 548, and see if a solution could come from that, but if you assume the lowest value is $40, and Sam has to be $40, and the 9 Mugs have to be $40 (because 9 comes first in your numbers), then there is already a clear discrepancy with clue 11, which says $40 is Sam or the Mugs, so $40 can't be both Sam and the Mugs.
We know from clue #2 that $40 is Sam, so Sam can't be drinking Mugs.
If it is true that Mugs (9) has to be the first digit, then the lowest cost can't be $40, it would have to be $35 or $30 to have a chance at being valid.
So, again, presetting the 961 548 combination in the grid, and starting with $35 as the lowest value, is there a valid solution? Yes, it appears there is, going straight down through the clues when you reach the last one, the grid is filled without conflict.
9 Mugs - $35 - Pippin - Stout
6 Humpens - $40 - Sam - Dark Ale
1 Pitcher - $45 - Frodo - Lager
5 Pints - $50 - Bilbo - Porter
4 Bottles - $55 - Merry - Pilsner
8 Tankards - $60 - Rosie - Hefeweizer
By the way, $30 as the lowest won't work with the numbers in this order, because that would put $40 on the third row with (1 Pitcher), which we know is Frodo (clues 1 and 9), but would also have to be Sam (clue 2),
So, with the given digits in that order, there appears to be only one possible solution.
But if you didn't know the "answer" ahead of time, there are multiple solutions to the logic puzzle. I don't understand if that is the goal. You have to find all the possible solutions, and then check each location to find the geocache, but the Logic Puzzle by itself will not lead you to a single location.
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