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LotR: Theoden

[Vala] Lord of the Rings riddles

Posted by _grayswandir_ on 03.11.2008 at 5.56.pm
Hey, folks! A few days ago, I posted a couple of LotR-related riddles in my journal, but I haven't had anyone come up with the answers yet. I figured I'd better give you guys a shot at them. ;) Sorry to those who see this twice!

Eowyn's Helm

One day in Rohan, King Théoden discovered a chest that had belonged to his father, Thengel. Inside, there were five helmets. Three of them were plated with silver, and two were plated with gold. Théoden called in Éowyn, Éomer, and Theodred, and showed them the helmets. He asked them to arrange themselves in a line. Theodred, at the back of the line, was able to see both of his cousins, Éomer and Éowyn. But Éomer, in the middle, could see only his sister Éowyn. Éowyn was in front, and could not see either of the men.

Théoden then proceeded to place a helmet, at random, on each of the youths' heads. Afterward, he asked Theodred whether he could tell what color his helmet was: gold or silver. Theodred could not tell. Théoden then asked Éomer whether he could tell what color helmet he was wearing. He admitted that he could not tell either. Finally, Théoden asked Éowyn whether she could tell which helmet she was wearing. She said yes, and named the color. She was correct.

What color helmet was Éowyn wearing, and how did she know?

A Dwarven Dilemma

Once, a party of thirteen Dwarves set out on a quest to kill a dragon. It was agreed between them that Thorin, their leader, would claim half of the riches, and the rest would be divided evenly among the remaining party members. Unfortunately, the plan did not entirely pan out. The dragon was destroyed, but soon neighboring communities of Elves and Men began demanding gold for themselves; and to make matters more confusing, Thorin and his two nephews were killed in battle. The result was a terrible disorder in the matter of distributing wealth.

Ultimately, each of the ten surviving Dwarves received a certain number of pounds of the dragon's gold; but now that they are headed home, there is no way for any of them to know how much gold was distributed all together, or whether the portions they received were equal. None of them is willing to tell the others (or anyone else) how much gold he received, for fear of being robbed. But each Dwarf wants very badly to know whether he has been cheated. Using only a bit of parchment and a quill, how can the ten Dwarves calculate the average number of pounds of gold they received, without divulging the amounts of their individual portions?


summonerluna at 2008-03-12 05:46 (UTC) (Link)

Still not sure on the second one, but as for the first...

Eowyn is wearing a Silver Helm. She knows this because:

There are only two gold helms, therefore she and Eomer cannot both be wearing gold, or Theodred would have known he was in Silver. If Eowyn were in gold, Eomer would have known his must be silver (for the same reasoning as before: if Theodred did not guess, then either Eomer or his sister or both must be in silver). Thus Eowyn would have known that both Eomer and Theodred must have seen at least one silver helm in front of them or they would have known the location of the two gold helms and could have guessed their own color.

I hope that reasoning makes sense...I solved it fairly quickly, but then it took me a bit of time to figure out how to word it. Cute riddles!
_grayswandir_ at 2008-03-12 21:12 (UTC) (Link)
Yep, exactly! :) And heh, yes, I agree that explaining the logic behind that one is more difficult than figuring the answer out. It sort of feels like you can't explain it -- like either you just intuitively get why Eomer's answer would be different if she were in gold, or... you don't. Anyway, I'm glad you got the answer!
Eámanë of Lothlórien©
farmhouse at 2008-03-16 14:18 (UTC) (Link)
I'm stumped on the second one :(
_grayswandir_ at 2008-03-17 00:17 (UTC) (Link)
Yeah, the second one's definitely harder than the first. Since it's been a while and nobody's got it, I'll just post the answer here.

So, the ten Dwarves have a piece of parchment and a quill. They pass these around in a circle, and each Dwarf writes down a random number of pounds of gold on the paper, and remembers what number he wrote. The tenth Dwarf adds all of the numbers together.

Then they pass the paper around again, and each Dwarf calculates the discrepancy between the amount of gold he actually got and the amount he wrote down, and adds or subtracts accordingly from the total. (For instance, if he received 100 pounds of gold, and wrote down 400 pounds on the paper, he would now subtract 300 from the total.)

After the total has been adjusted to correspond to the actual amounts the Dwarves received, they divide it by ten, and presto! An average. :)
Eámanë of Lothlórien©
farmhouse at 2008-03-17 17:12 (UTC) (Link)
I would have never guessed that haha

Oh and great riddles by the way!
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