Here, we have discussions and solutions for the puzzle part of our challenge:

The Shrines and Temples of Time

The tiny island of Eijiro is famous for its shrines and temples dedicated to the study of various aspects of time and the animals associated with those aspects, and well worth a visit to each. Determining the location of each shrine and temple, the year it was built, and its associated animal.

1. Of the temple in Usui and Matsuno Okura, one is dedicated to the cat and the other was built in 1585.
2. The shrine dedicated to the cat was built 120 years before the temple in Funai.
3. The temple dedicated to the mouse was built sometime before the shrine in Usui.
4. The temple built in 1825 isn't dedicated to the rooster.
5. Hori Takesi was built 60 years after the structure in Niwa.
6. The shrine in Niwa was built sometime after the temple dedicated to the frog.
7. Hori Takesi isn't in Toyagi.
8. Of the structure in Miyato and the temple dedicated to the cat, one was built in 1525 and the other is Matsuno Okura.
9. Sama Takako wasn't built in 1585.
10. The temple in Toyagi, Amari Michi, and the shrine built in 1645 are three different shrines.
11. Matsuno Okura was built in 1645.
12. Yamasaki is either the structure in Nakai or the structure dedicated to the dragon.
13. The shrine built in 1705 is either Yamasaki or the temple in Toyagi.
14. Amari Michi was built sometime before the temple dedicated to the frog.
15. Okabe Honzo is also a structure of note, and the dog one of the animals of time.
16. Can the construction year of one structure ever be known?

So, we have just over a week to submit an answer to this challenge.

Edit: So, I went ahead and made a grid for this of my own. Feel free to use it. I only have four of the 6 dates, listed, since the other two will have to be figured out later. (One is 120 years earlier than the Funai temple, the other is 60 years after the Niwa temple)...

New version with what I think are the other dates...

So, I've got the Matsuno Okura temple in 1645, dedicated to the cat, and sometime before the temple in Funai. Miyato's temple built in 1525. Usui's temple built in 1585. And the mouse sometime before Usui.
I've got more of it sketched out, but this is the only bit that's clear to me at the moment. (late....zzzz...)

edit: dude, I read 4 chapters of something before I came back and realized it Still hadn't posted this. After clicking 'post'. Has this happened to anyone else?

Yeah, I have: mouse, Miyato, 1525, Amari Michi cat, (Nakai or Niwa), 1645, Matsuno Okura frog, Usui, 1585, (Okabe Honzo or Sama Takako) Funai, 1765

But that's where I'm stuck...

I often have where I click post, and it spins forever without posting. Usually, though, if I open the board again in another tab, I find that it did actually post...

Okay, so I've worked through and worked through, and I think I've used up all the clues but the following:

12. Yamasaki is either the structure in Nakai or the structure dedicated to the dragon.
13. The shrine built in 1705 is either Yamasaki or the temple in Toyagi.

So anyway, since I couldn't make any progress, I decided to do an A and B version... I picked a spot where I had a fifty fifty shot of guessing right, made copies my sheet, and played out both versions of that fifty fifty shot....

For example, Hori Takesi was built in either 1705 or 1765. So I played through once choosing 1705, and once with 1765. Choosing 1765 didn't earn me a lot of progress. However, 1705 leads to an impossible conclusion. If I choose 1705, then work on, I eventually run into a situation that makes clue 13 impossible.
So, I conclude that Hori Takesi was built in 1765, and NOT in 1705. Doesn't gain much, but gains one more mark on the paper...

Did the same thing with 1585 being either Okabe Honzo or Yamasaki. If it's Yamasaki, we wind up with an impossibility, so it must be Okabe Honzo...

-_-" Whew! Well, I couldn't quite get the graph to work for me (I like little notes all over to help me remember stuff). So I've got about half a page of notes and lines and another page where I just drew a graph of my own. I've got about half the boxes filled as yay or nay.

:) Dat's ma' progress so far. (terrible english, but I'm Fried...)

...I should'a probably said what I have so far... tell me if this doesn't make sense..

1525-mouse-Miyato-AmariMichi 1585-frog-Usui- ? 1645-cat- ? -MatsunoOkura 1705- ? - ? - ? 1765- ? -Funai- ? 1825- ? - ? (Not Niwa)- ?

Whoo-wee! ^_^' That was a tricky one! This is what I have. Tell me how it compares to yours and whether you think it may be right. I'll try to type up my reasoning.

1525 - Miyato - mouse - AmariMichi 1585 - Usui - frog - OkabeHonzo 1645 - Nakai - cat - MatsunoOkura 1705 - Niwa - dragon - Yamasaki 1765 - Funai - rooster - HoriTakesi 1825 - Toyagi - dog - SamaTakako

:)

Well, let's see if I can explain any of this in a legible manner. :

From the information given, we have six places, six temples, six animals, and six years (1 of which has to be figured a little later).

Six Places: Funai, Niwa, Miyato, Toyagi, Usui, and Nakai

Six Temples: MatsunoOkura, HoriTakesi, SamaTakako, AmariMichi, Yamasaki, and OkabeHonzo

Six Animals: cat, dragon, frog, dog, mouse, and rooster

Six Years: 1585, 1825, 1525, 1645, 1705, and 1765 (through numbers 2 and 5 using addition and subtraction and the knowledge of two places)

Using an 18x18 grid (with three sections of 6 on two sides) we have this from the given information.

1525 - Miyato - mouse - AmariMichi 1585 - Usui - frog - ? 1645 - ? - cat - MatsunoOkura 1705 - ? - ? - ? 1765 - Funai - ? - ? 1825 - ? - ? - ?

I tried going through the whole chart with the assumption the number 13 had the shrine built in 1705 being Toyagi. Then I had to make an assumption that Yamasaki temple was in Nakai. This frame of thinking was proven wrong. With HoriTakesi ending up built in 1705, and Toyagi in 1705, then Niwa attempting to be the place of the temple in 1705; HoriTakesi proves that 1705 can NOT be Niwa. [Not sure if that all made sense, but I have a page and a half of sketches and notes to prove all this.]

With number 13 being "the shrine built in 1705 is either Yamasaki or the Temple in Toyagi" I guessed Yamasaki this time. That leaves only one year available to Toyagi, 1825. If you'll notice, each year, put in succession, is 60 years after each other. There are now 3 years still needing a temple, 1585, 1765, and 1825. HoriTakesi comes 60 years after the temple in Niwa. The only space available for HoriTakesi to go is in 1765 in Funai; making the 1705 temple, Yamasaki, in Niwa.

This makes the only place available to 1765 as Nakai; the only year available to SamaTakako as 1825; and OkabeHonzo in the year 1585. Lining up all the positive connections so far, we have:

1525 - Miyato - mouse - AmariMichi 1585 - Usui - frog - OkabeHonzo 1645 - Nakai - cat - MatsunoOkura 1705 - Niwa - ? - Yamasaki 1765 - Funai - ? - HoriTakesi 1825 - Toyagi - ? - SamaTakako

With this, we found Yamasaki is Not Naki, so it must be the temple of the dragon (also in 1705 at Niwa). Leaving the only option for the year the rooster temple was built as 1765; making the dog temple built in 1825.

I may have gone over my information twice somewhere in there. ^_^" But it gives us:

1525 - Miyato - mouse - AmariMichi 1585 - Usui - frog - OkabeHonzo 1645 - Nakai - cat - MatsunoOkura 1705 - Niwa - dragon - Yamasaki 1765 - Funai - rooster - HoriTakesi 1825 - Toyagi - dog - SamaTakako

Also, making the answer to number 16, "Can the construction year of one structure ever be known?" as YES. :)

^_^' Whew!

Wait so... is this one figured out? It's all gone over my head but if there's still things to be figured out I can take a crack at the updated graph if there is one?

O.O" Oh shoot! Do I have'ta figure out how to put the graph up here?!

Great job finishing the puzzle!