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### Solutions for Act V Scene 3 - A Way Out!

The title is a reference to the phrase "Seek a way out!", commonly heard in the game 999: Nine Hours, Nine Persons, Nine Doors. The characters depicted in the corners of each panel also come from this game. Combining this with the number of panels, as well as the dimensions of the grid of letters allows one to guess that the theme is the number 9. Even if this theme isn't immediately obvious, solving a few of the panels' minipuzzles should reveal this fact.

Top left

Every triangle has a nine-point circle which goes through the midpoints of each side, the foot of each altitude and the midpoints of the line segments from each vertex to the triangle's orthocenter. Constructing this circle for the given triangle and reading the letters inside, on and outside in rough clockwise/anticlockwise order gives RUGBY UNION POSITION.

Top middle

Each line describes a famous person with a birthday on the ninth of a month.

ClueFamous person Birthday
The 37th United States president Richard Nixon Jan 9
Casted as Loki in Thor Tom Hiddleston Feb 9
Twilight Saga's lead actress Kristen Stewart Apr 9
Pirates of the Carribbean actor, often in Burton films Johnny Depp Jun 9
Famously played Marty McFly Michael J Fox Jun 9
Played Gump and Robert Langdon Tom Hanks Jul 9
Most notable song is a cover of "I Will Always Love You" Whitney Houston Aug 9
Businessman who founded KFC Colonel Sanders Sep 9
Paul, George, Ringo and ...? John Lennon Oct 9

Using the birth months to index the names doesn't give anything useful, but indexing the slightly stilted clues gives TALESGAME.

Top right

The picture is of Richard Feynman (somewhat) pointing. This is a reference to a group of six nines in the decimal expansion of pi starting from the 762nd decimal place, colloquially referred to as the "Feynman point" despite debate as to whether the anecdote which led to this name holds any truth.

Inferring that the six red question marks correspond to the six nines, we can shift each of the letters by the following digits of pi to get MONOPOLYPROPERTYUK.

Middle left

This is a word search of words ending in NINE, but without the NINE part. The longer words such as STRYCH-NINE and MEZZA-NINE should be the easiest to spot.

Taking the unused letters gives SUMMEROLYMPICHOST.

Middle

Each line describes a pair of words differing by the letters IX.

blending dynasty mixing Ming
don cite Quixote quote
body part attach appendix append
number pen sixty sty
spiral norse being helix Hel

Indexing the longer word of each pair using the positions indicated by the red letters gives MONTH.

Middle right

Each image is a common word with a different meaning in cue sports, in particular nine-ball. The images are: DIAMOND, CUSHION, CUE (represented as pointing to cue cards), REST, POCKET, BREAK.

In nine-ball, each ball other than the cue ball has a number and colour. Using the colours of the image borders, mapping to numbers then indexing gives DOCTOR.

Bottom left

The image of short nails can be combined with NINE to discover that the panel's theme is the band Nine Inch Nails. The image, which looks like an album with a CD jutting out, is additional confirmation of this.

Going through songs by the band should reveal that each of the strings of dashes correspond to a ninth song of some album.

Album Ninth Song
The Slip The Four of Us Are Dying
Ghosts I-IV 9 Ghosts I
Hesitation Marks Various Methods of Escape
With Teeth Getting Smaller
Pretty Hate Machine The Only Time
Year Zero The Warning
The Downward Spiral Big Man With a Gun

Using the numbers to index the songs does not reveal much, but indexing the corresponding albums gives POKEMON.

Bottom middle

Each line is the sorted letters of a phrase containing NINE with the NINE part removed. This is easiest to see with the last line, since it is the shortest and doesn't have much in the way of anagrams.

The phrases are:

• A stitch in time saves (nine)
• (Nine) day wonder
• Cat o (nine) tails
• (Nine) times out of ten
• The whole (nine) yards
• On cloud (nine)

Taking the letters at the specified indices gives CIRCLEOFHELL.

Bottom right

Noticing that each equation lacks the digit nine and taking inspiration from the theme, we can surmise that each equation needs to be solved in base 9. The division lines are confirmation of this, e.g. 72 in base 9 is 65 in base 10, which is indeed divisible by 5 in base 9 (= 5 in base 10).

Solving each equation in base 9 then reinterpreting the results as base 10 integers yields MOONWALKER. For example, the first line is 4 + 8 which is 13 in base 9, and the thirteenth letter is M.

Putting it all together

Each minipuzzle's answer refers to a set of items, so naturally by the theme we want to take the ninth item of each set. Doing so gives items with nine letters in its name, which serves as confirmation:

• Rugby union positions: SCRUMHALF
• Tales games: (Tales of) INNOCENCE
• Monopoly properties (UK version) in order from Go: WHITEHALL
• Summer Olympic Games host cities (by Olympiad): AMSTERDAM
• Months: SEPTEMBER
• Doctors (corresponding actors from Doctor Who): (Christopher) ECCLESTON
• Pokemon: BLASTOISE
• Dante's circles of hell: TREACHERY
• Astronauts who have walked on the moon: JOHNYOUNG

We haven't used the 999 characters yet, and a little identification and research reveals that each of them are assigned a bracelet number at the start of the game, from 1 to 9. Indexing each ninth item by the corresponding numbers gives the letters:

 scrumHalf innOcence whitehaLl aMsterdam sePtember ecclestOn blAstoise tReachery johnyounG

The only nine letter anagram of these letters is LAGOMORPH, the rabbit AI who appears to the players as a hologram in the sequel of 999, Virtue's Last Reward. Note that if one looks around the outside of the grid, the word HOLOGRAM is spelt clockwise as additional confirmation that the outer letters are correct.

Design notes:
This was an idea I had last year that I did not manage to finish in time. With the release of Zero Time Dilemma in 2016, the last game in the trilogy after 999 and Virtue's Last Reward, it felt appropriate to finish off the nines puzzle for this hunt. Many minipuzzle ideas were locked in quickly, such as the find-a-word, the IX panel and the base 9 panel. However, without something to tie all the panels together for a last step, the puzzle was stuck.

After tossing around many 9-related ideas, including one which 999 game fans may have noticed is missing, it felt appropriate to have nine sets and take their ninth items. Unfortunately, trying to find ninth items which were nine letters long proved difficult, but after much research I managed to come up with a satisfactory set. I tried to ignore rankings, such as constellations by size (CENTAURUS) and avoided television show titles for which I'm sure there must be a 9-letter ninth episode for some series out there. The tie-in with 999 characters for indexing at the end came about since other ideas, such as a 9-queens puzzle for indexing, proved restrictive and did not yield a good thematic answer.

Unfortunately, despite the difficulty of finding appropriate sets, there were two ambiguities with the final chosen sets which were troubling. The first is that the Olympic host city of the ninth winter Olympiad is INNSBRUCK, also 9 letters long - this was resolved by rewriting the find-a-word to include the word "summer". The second, however, was particularly annoying to deal with since there wasn't a good succinct way of differentiating - as some teams may have noticed, it's that if you take streets rather than properties for the Monopoly message in the upper right (i.e. skip utilies and railways) you get BOWSTREET. Indexing obtains an E and the final step doesn't yield a nine-letter anagram as a result, but I did worry that it would be a stumbling block for some teams. This was one of the reasons why the HOLOGRAM clue was placed around the outside - the other, of course, was that having the panels in answer order would make the answer too guessable with only a few panels solved.

Once the sets were decided on and the messages were chosen, it came time to match puzzles with messages. The IX puzzle had to go to MONTH, due to the sheer lack of pairings possible, and the nine-point circle was used to take up one of the longer messages first. The messages were initially plural (e.g. MONTHS rather than MONTH), but since S couldn't be used in the base 9 puzzle as it corresponds to 19 (not a number in base 9), the messages had to be changed to refer to singular items. Lack of good words gave nine-ball the next shortest answer of DOCTOR, and the additive nature of the pi/Feynman panel meant that messages with A were harder to use, giving it the Monopoly message. After that, the rest of the puzzles were relatively unconstrained, if only due to the indexing steps used.