MIT Mystery Hunt 2020/The Dollhouse Tour

The Dollhouse Tour is a word-based puzzle from the round of the 2020 MIT Mystery Hunt. The puzzle contains a number of images and a grid layout depicting the floor of a dollhouse.

Solve Path
The images below the grid are the most obvious places to start. There are 22 of them in total, but 11 numbers in the grid, so one can reasonably assume that each number and associated room matches with two images.

The solver should eventually notice that the images can be paired up such that they represent the same object viewed from different angles, and then identify that object; as a check, the number of squares in both images should enumerate the letters in the object's name. For example, image 1 is a LAMP viewed from the side, while image 4 is the same lamp in a top-down view; these two images have four squares in total.

Each object can be associated to one of the eleven rooms mentioned in the puzzle; the LAMP is associated with the Living Room, for example. The objects' names can then be written into the floorplan to form a criss-cross. Next, one should turn to the squares, which can now be placed on the respective words in the criss-cross such that the footprints form one continuous path through the dollhouse. The assembly process will also place red squares on some letters, which when read in order spell out the answer.

Final Answer:

Puzzle Elements

 * Image Identification - The first step in the puzzle is to identify the objects below the grid.
 * Spatial Reasoning - Mental Rotation. The aforementioned images can be paired such that they represent the same object viewed from different angles; the images can now be identified as household objects. For example, image 1 is a lamp viewed from the side, while image 4 is the same lamp in a top-down view.
 * Criss-Cross - After associating each object with a room, the dollhouse's floorplan can be used as a standard criss-cross grid.
 * Jigsaw - Each image has a number of associated squares with footprints running through them. These can be placed on the respective word in the completed criss-cross to form one continuous path of footprints.
 * Marked Spaces - Some images have a red square. After the previous step, these red squares will overlap letters, which form the answer.