Getting the key in front of the cage in Silent Hill f will see you moving cages with lights by turning fox and rabbit statues. Talk of 'the two must face each other' and 'shading of light' clearly means doing something with the lights is key, but it's not entirely clear what. The malleable nature of this puzzle can be confusing too, where each statue controls multiple cages, letting you change their relationship to each other. Coming at the end of the objective to find Sakuko in Silent Hill f, which is a whole thing on its own, this is a lot. So I'll explain what's going on and help you solve it.
How to get the key in front of the cage in Silent Hill f
To get the key in front of the Cage in Silent Hill f you'll need to use four Statues, labeled here A to D to move pairs of Cages, 1-6, up and down. Each Statue will move through three positions, moving its pair of Cages between a high, middle and low level with each turn. The Statues control the following Cages in Silent Hill f:
A - 1 and 2
B - 3 and 5
C - 2 and 4
D - 2 and 6
The aim here is to line up all the Cages level with the walkway floor, and retrieve the lampshades inside Cages 2 and 5. The curveball being that while Statues A and B move their Cage pairs up and down in unison, Statues C and D move their pairs up and down in opposites (so while one goes up, the other goes down, etc).
I can't really give you a full solution here as the chances are you, like me, moved a bunch of Cages around before you realised what was happening. So we won't have a common starting point I can explain a solution from.
The key to solving this, however, is Cage number 2, as it's the only Cage controlled by more than one Statue, specifically Statues A, C and D. As you line up all the other Cages, keep an eye on Cage 2 and its relationship with Cages 1, 4 and 6.
You'll want to use either Statues C or D, in conjunction with A, to balance out all three Cages as you aim to get Cages 2, 4, and 6 level with the floor. It might take a little trial and error but eventually you should be able to get all six cages lined up at ground level.
When all the cages are level with the floor the middle two will open, letting you get the Restraint Lampshade and the Talon Lampshade. These can then be placed on the lanterns either side of the key, releasing it. Now you can return to the Grand Hall and use it to open the other set of Sacred Doors.
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