The Stone Cold Caves form the second puzzle in The Big, the Bad, and the Hungry, the first leg of the Logical Journey of the Zoombinis. It is to the northeast of the Allergic Cliffs, which it directly follows gameplay-wise.
Premise
There are four caves. The caves are arranged in a square shape, with one on the upper left, one on the upper right, one on the lower left and one on the lower right.
There is one path leading to each cave. The path on the far left leads to the upper left cave, the path on the far right leads to the upper right cave, the path on the middle left leads to the lower left cave and the path on the middle right leads to the lower right cave. To elaborate, the entrances to the paths are all roughly in one horizontal line, despite how some lead to a higher location than others.
There are four stone guards who regulate the rules to which Zoombinis are allowed to pass. The two smaller, brown-colored, classless stone guards control whether each Zoombini can go to the caves on the left or the caves on the right. One is situated between the far left and middle left pathways, while the other sits between the far right and middle right pathways. The two larger, gray-colored, refined stone guards control whether each Zoombini is allowed into the top caves or the bottom caves. One sits between the two top caves and the other sits between the two bottom caves. They change their rules every now and then.
When a Zoombini attempts to take the wrong way, the stone guard jumps into the air and lands heavily, sending a shockwave through the cobblestone pathway and knocking the Zoombini all the way back down. Enough of these shockwaves will eventually cause four large stones to fall at once, one blocking each pathway and signaling that no more Zoombinis are able to pass.
Solving the Puzzle
This puzzle is similar to the Allergic Cliffs, but rather than having two paths there are four. If a guard that decides left versus right rejects a Zoombini, the other guard that decides left versus right will allow that Zoombini. If any guard that decides top versus bottom rejects a Zoombini, the other guard that decides top versus bottom will allow it.
As you can see, this means that for each Zoombini there is only one path it can safely follow. The trend is determined by the Zoombinis' features, and so by observing what each stone guard will allow and what they will reject, conclusions can be drawn about the pattern.
Even in the harder levels, the player is given a greater number of tries in this puzzle than in any other, making it relatively easy to pass.