### Capital Craziness by Bob Lodge

This is like *March Madness*, but already at the semifinals, with only four teams remaining in the competition. Four separate puzzles will determine the score for each, and the two winners will then seed into the final game. Two more scores determine that outcome, so in all, six different puzzles must be solved. The six solutions will determine most of your score, but correct seeding, finding the winner, and bonus points will also be important.

The four teams are state capitals: __Austin____Boston____Concord____Denver__

**X** = A four-digit integer, containing the digits 1, 2, 3, and 4 in some order

**Y** = The __difference__ between the largest and smallest prime factors of X, which is composite

**Z** = The largest prime factor of Y, which is composite

Example: If X = 1234, then Y = (617 - 2), or 615, and Z = 41

To seed, use the value of X __for which Z is a maximum__. Write one digit under each letter, then enter each team into its corresponding slot in the diagram. The score for each team is the final answer (always a 2-digit integer, no ties) to that puzzle. When two winners are determined, enter them ALPHABETICALLY into positions 5 and 6 for the final game, the first into slot 5. Puzzles 5 and 6 determine the final championship game scores.

Stay alert! You never know when a puzzle might be dedicated to Grover Cleveland! J But watch for cross references, which can act as a two-way hint, helpful in either direction. They occur not only within puzzles but from one to another, and are not always acknowledged both directions. So, for example, if you are stuck on a clue in Puzzle 3, perhaps there is a reference to it in Puzzle 5 that will help. To facilitate references, separate items in puzzles 2, 5, and 6 will be labeled with *bold italic*** capital** letters, referred to as the

**.**

__key letter__

** Important**:

__Be sure to note the following reference formats, which will be used throughout the contest__:

* Reference to just a key letter (** G** ), refers to another item in the same puzzle.

* A # sign, number, dash, and key letter (example ** #5-G**) means the ANSWER to item

**in Puzzle #5.**

*G** If a ** c** is appended, as #

**, that refers to something in the CLUE for that item, rather than the answer.**

*5-Gc** A vague reference to “another clue” or “elsewhere” may be in either the same puzzle or a different one.

__Semifinals__*Seed 1-4 per above. Put winners into 5 and 6 alphabetically.*

* *

__# TEAM PUZZLE SCORE WINNER__

1 [__] __#1____(___)_

\_[_________]

2 [__] __#2____(___)_/ (to finals)

3 [__] __#3____(___)_

\_[_________]

4 [__] __#4____(___)_/ (to finals)

__Finals__

5 [__] __#5____(___)_

\_[_________]

6 [__] __#6____(___)_/ Winner!

** Puzzles:** Each puzzle presents its own challenge, but there is also much intermingling and cross referencing. They are:

#1 - ** Two Towns** - US geography, with ZIP codes and factoring

#2 -

**- extensive use of the Internet Movie Data Base**

*IMDB Inquest*#3 -

**- following complex instructions**

*Daunting Directions*#4 -

**- more geography, but worldwide. Get a good atlas.**

*Lost Lake*#5 -

**- a killer version, you make the grid.**

*Cryptic Crostic*#6 - ** Operation Obfuscation** -

*Daunting Directions*was just a warmup!

__ __

** Illustrations**: Puzzles

**#3**,

**#5**, and

**#6**utilize the 15 images, numbered in order of first appearance as

**[Fig xx].**

__ __

** Basic Scores**: Seeding 1-4 are 3 points each (easy 12 points). 5-6 are a little harder, 4 points each, for 8 more. Playoff winner is 5 points, so total possible so far is 25 points. The first correct score (solution to any puzzle) is worth 10 points, and each after that garners one more point, so all six can earn 10+11+12+13+14+15 = 75 points, grand total 100 points.

Note that a single wrong answer could lead to wrong seeding for #5 and #6 and the wrong winner, losing 15 + 8 + 5 = 28 points, and reducing total score to 72! Conversely, this means that any score above 72 may be a very strong contender, and Bonus Points could well be the decisive factor.

** Bonus Points**: Two types of bonus points are available. For each puzzle, one BP will be awarded to the

__first__correct solution received, but

__only for a given contestant’s first entry for that puzzle__, so a hasty unchecked entry, or a blitz of many guesses over a likely range, will likely fail.

At contest end, if any puzzle was correctly solved by __only one entrant__, __five__ BP’s will be awarded! So, a theoretical maximum score would be 136, but only if all 6 are correct on the first try and nobody else solves a single puzzle! (I expect winner in 72-110 range) Although an initial wrong answer disqualifies for the 1-point Bonus, in theory a correction and no other solvers could still garner the 5-point Bonus for the same puzzle! The 1 point will either not be awarded or go to the next eligible solver, even if the one with the wrong answer submits a correction first. Like the infamous *Jeopardy* buzzer, too quick and you lock yourself out!

** Entries**: You are encouraged to send a solution each time you think you’ve first solved a puzzle (any order OK), to try for a bonus point. Send all entries to [email protected] Be sure to include your name, and please always use the same email address (or acknowledge it if a quick try from elsewhere is desired). Subject of early bonus entries can be “Puzzle #2” etc, and message may show just the score (puzzle solution). Seeding of teams and winner may wait until final entry, of a simple list like this:

__Puzzle__ __Team__ __Score__

# 1 ___________ _____

# 2 ___________ _____

# 3 ___________ _____

# 4 ___________ _____

# 5 ___________ _____

# 6 ___________ _____

Winning Team: ____________

Subject should say “Final Entry”, but it may still be updated. Only the last received will count, even if a lower score than a previous one. Questions or comments should be posted publicly on the board, but please, no “spoilers”! Send email if you fear you might divulge too much, but whenever possible I will respond publicly to avoid any inside advantages.

** Ignore this comment** unless you have knowledge of a technical argument at the final step of one puzzle, that would raise its answer by

__one__. Most are unaware of it, and no other outcomes would be affected, but to avoid any unnecessary concern, either answer will be accepted.