14
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There's a tower in a far off land, one that you can only climb by unlocking the secret password to all the floors. Each floor has an inscription on the walls, indicating a number. As you approach a bird screeches at you:

I sit upon this enigmatic wall.

At the top is the first floor of them all.

To reach me you'll need primal instinct.

Each floor requires a number that is distinct.

The bird then turns to stone, and becomes part of the building once again:

 __,---.
/__|o\  )
`-\ / /
  ,) (,
 //   \\
{(     )}
=""===""=
|......_|   (1) ~ *SQWUAK!!* At the top is the first floor of them all *SQWUAAAAAAK!!*
|......-|
|....._.|
|....._-|
|.....-_|
|...._.-|
|....___|
|...._--|
|....-._|
|....-_-|
|..._..-|
|..._.__|
|...__._|
|...___-|
|...__-_|
|..._-.-|
|..._---|
|...-._-|
|...-.-_|
|...-___|
|...-_--|
|...--._|
|...---_|
|.._...-|
|.._..--|
|.._._-_|
|.._.-.-|
|.._.-__|
|.._.---|
|..__.._|
|..__._-|
|..__-._|
|..__-_-|
|.._-..-|
|.._-.__|
|.._-__-|
|.._-_-_|
|.._--__|
|..-..._|
|..-.._-|
|..-._.-|
|..-._--|
|..-.-._|
|..-_..-|
|..-_.__|
|..-_.--|
|..-__._|
|..-_-__|
|..--.-_|
|..--_.-|
|..--___|
|..--_--|
|..---_-|
|..----_|
|._...--|
|._..__-|
|._..-.-|
|._..---|
|._._.._|
|._._.-_|
|._.__.-|
|._.____|
|._._-_-|
|._.-_._|
|._.-__-|
|._.-_-_|
|._.--.-|
|.__..-_|
|.__.___|
|.__.-_-|
|.__.--_|
|.___..-|
|.___.--|
|.____-_|
|.___-__|
|.__-.._|
|.__-._-|
|.__-_.-|
|.__--._|
|.__--_-|
|._-..__|
|._-.__-|
|._-._-_|
|._-.---|
|._-_.._|
|._-_.-_|
|._-__.-|
|._-__--|
|._-_--_|
|._--..-|
|._--.__|
|._--.--|
|._---.-|
|.-...._|
|.-..._-|
|.-..___|
|.-.._--|
|.-..-_-|
|.-._.--|
|.-.__._|
|.-.-.._|
|.-.-.-_|
|.-.-_--|
|.-.--_-|
|.-_...-|
|.-_..__|
|.-_._._|
|.-_.-.-|
|.-_.---|
|.-__._-|
|.-__.-_|
|.-_____|
|.-__-._|
|.-__-_-|
|.-__--_|
|.-_-_._|
|.-_--.-|
|.-_--__|
|.-_----|
|.--.._-|
|.--._.-|
|.--.___|
|.--.--_|
|.--_..-|
|.--_.--|
|.--__-_|
|.--_---|
|.---.-_|
|.---_--|
|.-----_|
|_....__|
|_..._._|
|_...__-|
|_...-__|
|_.._.._|
|_.._._-|
|_..____|
|_..__--|
|_..-.__|
|_..-__-|
|_..----|
|_._..._|
|_._._.-|
|_._.___|
|_._._--|
|_._.-._|
|_.__..-|
|_.___-_|
|_.__-.-|
|_.__-__|
|_.__---|
|_._-___|
|_._-_--|
|_._--._|
|_._--_-|
|_.-._-_|
|_.-.-.-|
|_.-_.._|
|_.-__.-|
|_.-_-._|
|_.-_-_-|
|_.--..-|
|_.--.--|
|_.---__|
|_.-----|
|__..._-|
|__.._.-|
|__..-._|
|__..--_|
|__.__._|
|__.___-|
|__._-.-|
|__._-__|
|__.-._-|
|__.-.-_|
|__.-___|
|__.--_-|
|__.---_|
|___..--|
|___._._|
|___._-_|
|____.-_|
|_____.-|
|_______|
|_____--|
|____-_-|
|___-..-|
|___-_._|
|___-_-_|
|___--__|
|__-._--|
|__-.-._|
|__-_..-|
|__-__._|
|__-_-.-|
|__-_---|
|__--._-|
|__--___|
|__----_|
|_-....-|
|_-...--|
|_-..__-|
|_-.._-_|
|_-..-__|
|_-._.-_|
|_-.__--|
|_-.-.--|
|_-.-_._|
|_-.-__-|
|_-.--.-|
|_-.--__|
|_-_..._|
|_-_.._-|
|_-_..-_|
|_-_._.-|
|_-_.-_-|
|_-_.--_|
|_-__.__|
|_-_-_.-|
|_-_-_--|
|_-_--_-|
|_--..__|
|_--.-__|
|_--_._-|
|_--_-._|
|_--_-_-|
|_--_--_|
|_---..-|
|_---.--|
|_---_-_|
|_----.-|
|_----__|
|-....._|
|-...___|
|-...-_-|
|-...--_|
|-.._..-|
|-.._.__|
|-.._.--|
|-..___-|
|-.._---|
|-..-_.-|
|-..--._|
|-._..__|       ______ This is you.
|-._._._|      /       You're a brave warrior.
|-._.__-|     |
|-._.-.-|     V
|-.__.._|   \_o_>
|-.__._-|    `|'
|-._____|    /^\ 

Your quest is to climb the tower and slay the bird. He's told you the number you need for the 250th floor, but you'll have to figure out the rest. There may be more to what he said, there's most likely a pattern because he mentioned how each number should be distinct! Figure out the pattern and you can slay that pesky bird that crapped on the kings carriage.

$\endgroup$
17
$\begingroup$

Notice that

Each symbol in the tower is either . _ or -, what can hint us that base three counting is included. If we know that the top florr is 1, than we can replace . with 0, _ with 1 and - with 2. This indeed yield correct base 3 numbers, which I converted back to base 10.

With this method, you can climb the tower:

       ______ This is you,
      / now on the top of the tower
      |
     V
  \_o_>
    |' /^\ |000001| |000002| |000003| |000005| |000007| |000011| |000013| |000017| |000019| |000023| |000029| |000031| |000037| |000041| |000043| |000047| |000053| |000059| |000061| |000067| |000071| |000073| |000079| |000083| |000089| |000097| |000101| |000103| |000107| |000109| |000113| |000127| |000131| |000137| |000139| |000149| |000151| |000157| |000163| |000167| |000173| |000179| |000181| |000191| |000193| |000197| |000199| |000211| |000223| |000227| |000229| |000233| |000239| |000241| |000251| |000257| |000263| |000269| |000271| |000277| |000281| |000283| |000293| |000307| |000311| |000313| |000317| |000331| |000337| |000347| |000349| |000353| |000359| |000367| |000373| |000379| |000383| |000389| |000397| |000401| |000409| |000419| |000421| |000431| |000433| |000439| |000443| |000449| |000457| |000461| |000463| |000467| |000479| |000487| |000491| |000499| |000503| |000509| |000521| |000523| |000541| |000547| |000557| |000563| |000569| |000571| |000577| |000587| |000593| |000599| |000601| |000607| |000613| |000617| |000619| |000631| |000641| |000643| |000647| |000653| |000659| |000661| |000673| |000677| |000683| |000691| |000701| |000709| |000719| |000727| |000733| |000739| |000743| |000751| |000757| |000761| |000769| |000773| |000787| |000797| |000809| |000811| |000821| |000823| |000827| |000829| |000839| |000853| |000857| |000859| |000863| |000877| |000881| |000883| |000887| |000907| |000911| |000919| |000929| |000937| |000941| |000947| |000953| |000967| |000971| |000977| |000983| |000991| |000997| |001009| |001013| |001019| |001021| |001031| |001033| |001039| |001049| |001051| |001061| |001063| |001069| |001087| |001091| |001093| |001097| |001103| |001109| |001117| |001123| |001129| |001151| |001153| |001163| |001171| |001181| |001187| |001193| |001201| |001213| |001217| |001223| |001229| |001231| |001237| |001249| |001259| |001277| |001279| |001283| |001289| |001291| |001297| |001301| |001303| |001307| |001319| |001321| |001327| |001361| |001367| |001373| |001381| |001399| |001409| |001423| |001427| |001429| |001433| |001439| |001447| |001451| |001453| |001459| |001471| |001481| |001483| |001487| |001489| |001493| |001499| |001511| |001523| ______ This is the beheaded bird. |001531| / |001543| | |001549| V |001553| |001559| ,)(, |001567| // \\ __,---. |001571| {( )} /__|o\ ) |001579| =""===""= \-\,,/,,,,/

And the pattern:

the floors are numbered with prime numbers

$\endgroup$
  • 5
    $\begingroup$ Except one (1). $\endgroup$ – Arnaud Mortier Mar 24 at 0:10
  • $\begingroup$ Hah! I love the art additions, and whoops... I always forget whether or not 1 is _________. :( $\endgroup$ – Magic Octopus Urn Mar 25 at 11:57

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