The collection of puzzles above all share the same underlying structure: you’re given two (or more) types of “things” (animals, vehicles, robots, etc.) and a set of aggregate counts (legs, wheels, heads, biscuits, hands). To crack these problems, we translate each “type” into a variable and each aggregate count into a linear equation.

Step 1: Define your variables. For example, let C = number of cats, P = number of parrots, D = number of dogs. Each variable represents one “group” whose contribution you know per item (e.g. cats have 4 legs, parrots 2 legs).

Step 2: Write one equation per total. If you know the total number of legs is 30, and each cat and dog has 4 legs while each parrot has 2, you’d write:

    4C + 2P + 4D = 30
  

If you also know the total of animals, wheels, heads, biscuits, or any other count, write an equation for each:

    C + P + D = total animals
    2W₂ + 3W₃ = total wheels
    … and so on.
  

Step 3: Solve the system. Use substitution or elimination to find integer solutions (non-negative whole numbers). Because these are “real” objects, we only accept answers where each variable is a non-negative integer.

Step 4: Interpret your result. Once you have C, P, D, etc., verify they satisfy all original conditions. This approach guarantees a clear, step-by-step path from problem statement to solution.

Tip: When more than two variables appear, look for extra constraints (total count, parity, or divisibility) to reduce possibilities. These “counting riddles” are simply applications of basic algebra-fun, engaging, and a great way to practice translating words into equations!