[quote=Optimatum]I wonder if there’s some exact sequence of successes and failures that would let you skip some number of the optional steps and get Who is Salt? without selling everything.[/quote]Your post inspired me to run some numbers, though I haven’t yet tried it out with a character. In short, there should be a number of possible paths, though not all of them are practical.
There are only two results on Winking Isle that will reduce the one’s place of your Fasting and Meditation: failing Watch the Well (-385) and failing Inhale the Scents (-1925). The wiki states that you need exactly 111 F&M to unlock the option for obtaining the Sun Beneath the Sea, so this means that we have to begin at F&M 101 (because we can’t begin at 66). As a result, our goal with all the fasting and meditating is to get a net increase in F&M of 10.
Luckily, Winking Isle is really easy to work with mathematically. Every success increases F&M by a multiple of 50 and every failure decreases F&M by a multiple of 385. This means we can simplify the whole of Winking Isle into the expression:
50x - 385y
where x is based on the number of successes
and y is based on the number of failures.
The equation most literally asks "What will be your net change in F&M if you succeed at waiting by the well x times and fail at watching the well y times", but practically, we can just say (mathematicians forgive me) that different actions will increase x by different integer amounts. For instance, succeeding at Looking Up is the equivalent of increasing x by 200 while failing at Looking Up is the equivalent of decreasing y by 20.
Every interaction on Winking Isle follows this basic idea. If we were to write the formula as 500x - 385y, basically pretending that waiting by the well doesn’t exist, x and y would increase at the same rate per action. Succeeding at Looking Up would then increase x by 20 while failing still decreases y by 20. The artist in me greatly appreciates the symmetry here, but we need to work with 50x - 385y instead to fully represent the experience of fasting and meditating.
Anyway, we just solve this formula for 10 to output the results we want:
50x - 385y = 10
The result is two simple equations, both of which must be satisfied.
x = 77n + 31 AND y = 10n + 4
where n is an integer.
The lowest action cost is where n = 0, which is to say that x = 31 and y = 4. In other words, you have to gain 31 * 50 = 1550 F&M and lose 385 * 4 = 1540 F&M, which is equivalent to succeeding at Watch the Well three times, failing it four times, and waiting by the well once (though not in that order, of course; your last step has to be a failure).
However, for any integer n, you can output a result. For instance, you can gain 5400 F&M and lose 5390 F&M (n = 1), or you can gain 9250 F&M and lose 9240 (n = 2), etc. These are all possible ways of gaining that additional +10 F&M you need to go from 101 to 111 without paying the price. There is technically an infinite number of ways to do this, but it’s impractical, to say the least.
If someone were to do this, they wouldn’t need to sell their Wild Words, but everything else would still have to go. If the character were to turn back at the Gate, this might be useful, but unless they had absolutely enormous stocks of Wild Words before Winking Isle, it’s probably not the best use of actions. But it is possible, and that’s pretty neat.
Bonus Information:
[spoiler]Using this formula, you can also give greater mathematical backing to the statement that you have to begin with 101 F&M for this to work:
50x - 385y has no integer solutions for (111 - 77 = 34), (111 - 88 = 23), or (111 - 99 = 12), which are the only other possible starting points. This is to say that it’s impossible to reach exactly F&M 111 from any of those numbers. Of course, this is assuming that you need exactly 111 to gain the Sun Beneath the Sea, but I trust the wiki in this matter.
Other fun facts:
- It’s impossible to reach exactly 10,000 or 60,000 F&M, because you’re starting with at least 77 F&M.[/li][li]The lowest F&M above 60,000 that you can reach having failed at least once is 60,002, though it’s practically impossible to reach. This is represented by the equations:
x = 77n + 1237 AND y = 10n + 5
And that’s about it.[/spoiler]