Riddle 1: Competitors are knocked out in sequence. Reword the given information into A>B relationships, then you can trivially use the transitive properties of inequalities (ie: if A beat B, then A beat everyone B beat, too) to determine the order.
FL > PP > AA > ZO > MH > JR > GG > TS > BB > KB
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Frodo Lightmantle beat all other named competitors, so unless it's a trick question where there were more participants than named, Frodo is the "Prince of Ale", followed by Peltasar Piper, Alan Ardman, Zach Oremaster, Marrian Hammerfall, Jarlaqusel Rench, Graham Goodfellow, Tom Stonehand, Brian Brick, and finally Krensh Bigfingers in last place.
Riddle 2: Simple algebra.
The three dwarves had 39 pieces of ore between them (although it's impossible to tell how many pieces each had of gold, silver, iron, and tin ore).
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H-6+1 = 1/2*(J+6-1)
D-14+1 = 1/3*(H+14-1)
J-4+1 = 1/6*(D+4-1)
H+D+J=?
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2H-15 = J
3D-52 = H
6J-21 = D
J = 6D - 119
J = 36J - 245
35J = 245
J = 7
D = 21
H = 11
H+D+J=39
Riddle 3: It's a trick question.
There is no "remaining 1 gp". The riddle is intentionally misleading you. Each traveler paid a net of 9 gp, for a total expenditure of 27 gp. 25 gp went to the inkeeper Farlin and 2 gp went to his wife Shantal's pockets.
Riddle 4: Somewhat more complex series of interactions. Since there are only 5 spaces for each dwarf, herb, or cooking method, and each space can only have one item from each category, going through the clues one at a time quickly narrows down the possibilities.
First, Iridor is Fried with Melon.
Second, Sharnor is served Raw with Coriander.
Third, Armin is Baked with Garlic.
Fourth, Ormus is Steamed with Cucumber.
Fifth, Etna is Grilled with Ginger.
Then again, since the dwarves broke free and slew the ogres, none of them were actually cooked in any order with any herbs in any way.
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Armin can't be 1st or 5th (ie: must be 2nd, 3rd, or 4th).
Two dwarves (Iridor and the one served Raw) are before Armin.
- Armin can't be 2nd. Armin must be 3rd or 4th.
- Iridor must be 1st or 2nd.
- Raw must be 2nd or 3rd (and not Iridor or Armin).
Cucumber is the 4th dwarf's seasoning. The 4th dwarf cannot be Grilled.
Ormus must be Grilled or Steamed. Ormus is not seasoned with Ginger.
Iridor is 2 places ahead of the Garlic dwarf.
- Since Iridor is 1st or 2nd, Garlic must be 3rd or 4th. However, Cucumber is 4th, so Garlic must be 3rd.
- Iridor must be 1st.
Etna is not cooked Fried or Raw. Etna is not 4th.
Melon is 1 place before Coriander.
- The only two adjacent openings for herbs are 1st and 2nd.
- Melon is 1st.
- Coriander is 2nd.
- The last remaining herb, Ginger, is 5th.
- Ormus can't be 5th.
Baked is 3rd. Coriander and Ginger are not 3rd.
- Raw can't be 3rd. Raw must be 2nd.
- Etna can't be 2nd. Etna must be 3rd or 5th.
- Ormus can't be 2nd or 3rd. Ormus must be 4th.
- Armin can't be 4th. Armin must be 3rd.
- Etna can't be 3rd. Etna must be 5th.
- The last remaining dwarf, Sharnor, is 2nd.
- Cucumber can't be Grilled. Ormus must be Grilled or Steamed. Steamed must be 4th.
- Etna can't be fried. Grilled must be 5th.
- The last remaining cooking method, Fried, is 1st.