Contest 3: Four-Puzzle Derby

Note: this contest was delayed by eleven hours, because although I'd scheduled this post to go up automatically at 12:00 AM on 11/30/10, apparently Blogger thinks the day starts at 12:01 AM and ends at 12:00 AM. Stupid Blogger.

Do you want to win high-quality logic puzzles imported from Japan? The Four-Puzzle Derby contest might be your opportunity to do just that!
Some of you may recall my previous contests Attack of the Four Puzzles! and Attack of the Four Puzzles II!; this contest is similar, but I've decided to mix things up by adding in elements from the Nikoli Derby. The four short sections below explain all of the details.

How to enter:
This contest combines a four-part logic puzzle (below) with a horse race. To participate in the contest, simply send an e-mail to glmathgrant[at]gmail[dot]com. Your entry should consist of the following:
a) the final answer to the four-part puzzle below, obtained from part iv;
b) the name of the horse you'll be entering in the race (this is just for fun and has no effect on the final outcome, so don't stress out over it too much);
c) the number of the gate your horse will start from (any integer between 1 and 50 inclusive).

Only one entry is allowed per person, but you may change your entry at any time before the deadline, 11:59 PM (Central time) on December 14, 2010.

How to win:
After the deadline has passed, the winner will be determined as follows:

a) Anyone who submits an incorrect answer to the four-part puzzle below will have his or her horse disqualified from the race.
b) If two or more qualifying horses start from the same gate number, then their riders will all fall off of their horses before finishing the race. (Heck if I know why.)
c) The remaining horses will all run the whole distance, and finish the race in order from the lowest-numbered gate through the highest-numbered gate.

Thus, to win, you must submit a correct answer to the four-part puzzle, and choose the lowest-numbered gate that nobody else with a correct answer has chosen.

In the event that none of the horses finish, the winner will be selected by random draw from all of the qualified entrants, without regard to the gates from which they started. If no horses even qualify (that is, nobody sends a correct answer), then no prize will be given.

In addition, a booby prize will be awarded to the entrant whose horse finishes in second-to-last place. If only two horses finish, then the booby prize will be awarded to the second place finisher. If only one horse finishes, or none do, then the booby prize will not be awarded.

The winner will receive his or her choice of either 3 of Nikoli's Pencil Puzzle Books, or any 1 or 2 Nikoli books whose prices total at most 2100 yen (see this link for a list of all of the books Nikoli has available). Each Pencil Puzzle Book contains about 96 puzzles of one particular type, which is great if there's a certain puzzle type you particularly want to focus on; if you'd rather have a wider variety of puzzles available, books like the Penpas Mix series, the Puzzle Box series, and the Puzzle the Giants series will satisfy your needs perfectly. Either way, you win! :) When you win, provide me with your mailing address and which books you'd like; I'll pay Nikoli to ship them directly to you.

The booby prize will not be revealed until the outcome of the contest is decided, but it is worth far less, and far less puzzle-related, than the Nikoli puzzle books. It will be shipped from Abilene, TX (where this blog is headquartered).

By entering the contest, you agree to the following terms:
a) You agree not to discuss your entry with any other entrants or potential entrants until the contest is over.
b) You agree to provide me with a mailing address in the event that you win. (In return, I agree not to use your mailing address for any malicious purposes, such as sending junk mail or other undesired things.)
c) You agree to wait patiently for your prize to arrive, without moaning or kvetching, especially if it's being shipped from a different country than where you live (such as winning the Nikoli books if you don't live in Japan, or the booby prize if you don't live in the United States).

Now that you're done reading all that, here is the four-part contest puzzle. Good luck! :)

Part i. Room and Reason

Solve the Room and Reason puzzle below (rules of Room and Reason).
How many black cells and how many white cells are there in the indicated row? These are the respective values of B and W in Part iii below.

Part ii. Fencing Match

Solve the Fencing Match puzzle below (rules of Fencing Match).
How many 0's are inside the loop, and how many 0's are outside it? These are the respective values of I and O in Part iii below.

Part iii. Quad-Wrangle

Using the values for B, W, I, and O derived in Parts i and ii, solve the Quad-Wrangle puzzle below (rules of Quad-Wrangle).
What are the sizes of the rectangles containing i, ii, iii, and iv? These are the respective values of i, ii, iii, and iv in Part iv below.

Part iv. Polyominous

Using the values for i, ii, iii, and iv derived in Part iii, solve the Polyominous puzzle below (rules of Polyominous).
The five numbers in the lettered cells, taken in reading order (a, b, c, d, e), form the final answer. Send this final answer, as well as your horse's name and starting gate, to glmathgrant[at]gmail[dot]com to enter the Four-Puzzle Derby contest.

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