The treehouse puzzle has a problem. The information given is incomplete: we have three equations in four unknowns. Despite this, it can approximately be solved, as the loot in the four houses can be broken down mostly into the combinations with known values, adding to 66, with one object left over. Assuming all values are greater than or equal to one, the one left-over object must have value 1, 2, 3, or 4 since one combination it is in adds to 5. The other it's in has it with two copies of another object adding to 10, so it must be an even number: 2 or 4. The total then comes to either 68 or 70. However, nothing triggers when either of those is input. In case the "example objects" count, adding an extra 21, I also tried 89 and 91. Nothing triggered in response to those either.
So, 2 things are broken: missing information; and the correct answer (whichever of the 4 possibilities I narrowed it down to is actually it) doesn't trigger anything when input.