Logic Problem: Troll Bridges of Madison County

St. Theresa · 03-22-2004, 10:43 PM

Can you figure this out?

Quote:

Although not normally civic minded, the trolls of Madison County turned out in record numbers to lobby the state senate for the construction of additional bridges in their area. It seems that there are simply not enough bridges to accommodate the burgeoning troll population in the six towns that constitute Madison County. Each town, in fact has only one bridge (each of which is a different type--one is a suspension bridge), which has forced the county's 26 trolls to share quarters, certainly not a trait for which they are well known! With the troll population expected to triple over the next decade, the impassioned trolls insist that they will need government support in order to navigate the trouble waters ahead. From the information provided, determine the trolls (three are Celegorm, Ngoldo, and Ufthack) who inhabit each town's bridge.

1. No bridge houses more than seven trolls, and no troll has a bridge to himself or herself. The simple-beam bridge, which isn't the one Huor calls home, houses fewer trolls than the arch bridge (which isn't where Jithidin lives) but more trolls than the one in Ocean Hill (which isn't Durthang's home). Alduya lives beneath the truss bridge.

2. The bridge in Corona, which is home to either exactly one troll more or exactly one troll fewer than Ivorwen's bridge, houses wither exactly one troll more or exactly one troll fewer than Zaragamba's bridge. Radbug lives with either exactly one troll more or exactly one troll fewer than Khelek does.

3. The bridge in Woodhaven houses exactly two more trolls than Tharbad's bridge (which is inhabited by exactly twice as many trolls as the bascule bridge) and exactly three more trolls than the one under which Yuldar lives. Huor doesn't live under the bascule bridge.

4. Phurunargian lives in the township of Fort Greene. Baragund doesn't share his bridge with Valinor.

5. Findegil doesn't live underneath the cantilever bridge. The bridge is Brighton houses either exactly one troll more or exactly one troll fewer than Galadrield's bridge, either exactly two trolls more or exactly two trolls fewer than Jithidin's bridge, and either exactly three trolls more or exactly three trolls fewer than Edrahil's bridge (which isn't the bridge located in Astoria.)

6. Losgar doesn't live with exactly two fewer trolls than his friend who lives under the cantilever bridge. Baragund (who doesn't reside beneath the arch bridge) doesn't share his shelter with fewer trolls than his cousin who lives beneath the arch bridge.

7. Huor's bridge is inhabited by exactly half as many trolls as the one that houses exactly one troll more than Quendi's bridge. Neither Ivorwen's bridge or the truss bridge is the one under which Valinor lives.

8. Wilwarin's dwelling can be found under the cantilever bridge. Othar lives with either exactly two trolls more or exactly two trolls fewer than Quendi, whose bridge houses fewer trolls than the cantilever bridge.

9. Durthang lives with fewer trolls than Galadriel. The bridge in Astoria, which doesn't have the fewest residents, is home to either fewer trolls or the same number of trolls as the one under which Khelek lives. Zaragamba doesn't live in Astoria, which isn't Malvegil's home town.

10. Silpion's bridge has fewer inhabitants than both Malvegil's bridge and Findegil's bridge but more inhabitants than the bridge that is home to exactly one troll more than Othar's bridge. Losgar, who doesn't live with Radbug, shares his bridge with either exactly one troll more or exactly one troll fewer than Xalme.

Um, yeah.

So basically, there are six towns, six bridges (one for each town) and 26 trolls. Incidentally, each troll's first name begins with a different letter of the alphabet, so you can just use "A, B, C" if you get out some paper to try to figure this out.

I'm not done solving this yet (it's driving me nuts.) I think I know exactly how the trolls are divided under the six bridges, and how many trolls are under four of the six. I know how many trolls live under one bridge in one particular town. I know how many trolls Huor, Quendi, Othar, Silpion, Tharbad, Alduya and Yuldar live with. But that's about as far as I go.

Any brainiacs gonna take a stab at this?

WARN before you give answers, or I will have to stab you with the jagged point of a blue Papermate.

PrinceFamiliar · 03-23-2004, 12:16 AM

I"m giving this a go. I'll let you all know later!

instant piano · 03-23-2004, 12:17 AM

There are too damn many trolls with unpronouncable names!

I'm printing this sucker off and making a chart...

St. Theresa · 03-23-2004, 10:14 AM

Quote:

I"m giving this a go. I'll let you all know later!

Yay!

Quote:

There are too damn many trolls with unpronouncable names!

I'm printing this sucker off and making a chart...

A,B,C, etc. works for the names.

The puzzle gives you a chart, but really it's just six rows and three columns, which doesn't help me. I use legal size paper...LOTS of it.

And I still haven't gotten it, but I won't cheat. Maybe I can convince Rob to post the answers if someone wants them but I'm not ready for 'em.

By the way, I was wrong about what I thought I knew last night. Now I *think* I know the REAL way the trolls are divided amongst the bridges, but I'm still about 19 trolls away from figgerin' in out.

Charles: · 03-23-2004, 11:53 AM

Hell, I can't figure out which ones are troll names and which ones are town names...

TheSkeptic · 03-23-2004, 12:32 PM

ill definitely have a go at this later. I lurve logic problems

Matt

St. Theresa · 03-23-2004, 12:38 PM

Bridges: Bascule, Simple-Beam, Suspension, Truss, Arch, Cantilever.

Towns: Ocean Hill, Fort Greene, Brighton, Corona, Woodhaven, Astoria.

Trolls: A, B, C...X, Y, Z

Number of trolls under any given bridge: 2-7, though not 2, 3, 4, 5, 6 and 7 (they must add up to 26!)

Mordecai · 03-23-2004, 04:11 PM

Woodhaven REPRESENT!

St. Theresa · 03-23-2004, 04:13 PM

I *think* I now know how many trolls live under each different type of bridge, a town or two, and a handful of trolls. Still working when I get the chance.

by the woods · 03-23-2004, 04:22 PM

Thanks for the logic problem! My brain needs a good distraction today.

St. Theresa · 03-23-2004, 04:53 PM

Sharsies....not the solution...just some of what I've figured out so far.....

PrinceFamiliar · 03-23-2004, 08:42 PM

I gave up on this totally. LOL. I did find out how many trolls under each bridge, but didn't get as far as the types and towns and which trolls beyond one or two.

Chris

St. Theresa · 03-23-2004, 08:58 PM

I did it! I did it!

Once I figured out how many trolls were under each type of bridge, I made a chart for the trolls and the numbers of trolls for process of elimination, kept going over the clues. The towns fell into place and then the last 7 trolls and I DID IT!

whirlygirl · 03-23-2004, 09:01 PM

I love this kind of stuff....

St. Theresa · 03-23-2004, 09:06 PM

Quote:

Originally Posted by whirlygirl

I love this kind of stuff....

Me, too. I ordered a set of about six logic problems issues from Penny Press for something ridiculous like $10 delivered. The particular puzzle type in this thread is one I usually wimp out on. I usually stick to the ones where you can actually use a grid chart. I especially cringe at the "either or" clue puzzles like this. So, I bes proud I figgered 'dis out.