To begin extrapolating what a 4-tree of footprints would look like, I could first use problem decomposition to assess what the “Footprints” challenge was asking for, and from this I determined that I would need to look for patterns within the examples given for 1-, 2- and 3-trees and then use those patterns to predict a 4-tree. When recognizing patterns, I noticed that each tree had a “trunk” made up of a column of footprints as many footprints long as the number in the tree’s name; for a 2-tree, it was two footprints, for a 3-tree it was 3 footprints, and so on, and then above the “trunk,” two versions of the previous tree (for a 3-tree, this would be two versions of 2-trees) branched out from the trunk. Knowing this, I could create an informal model for future trees and predict that, for any tree, the number in the title of the step would match the number of footprints in the “trunk” and then two branches identical to the last tree in the sequence would branch out from that “trunk.” Algorithmically, to find a 4-tree and solve the challenge (it was multiple-choice,) I needed to first find the answer which had a “trunk” made up of the correct number of footprints (based on my model) and then look for the tree, of those options, that had two branches, each identical to the last tree in the sequence.
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