1. The problem asks to show the structure when three letters $A$, $B$, and $C$ multiply each other, with each letter multiplying all letters in the sequence. 2. This means we want to find the product of all possible pairs and triplets formed by $A$, $B$, and $C$ in sequence. 3. The multiplication sequence includes: - Single letters: $A$, $B$, $C$ - Products of two letters: $AB$, $BC$, $AC$ - Product of all three letters: $ABC$ 4. Writing all these out, the full structure is: $$A + B + C + AB + BC + AC + ABC$$ 5. This expression shows every letter multiplied by every other letter in the sequence, including the single letters themselves. 6. This is a common way to represent the expansion of the product $(1 + A)(1 + B)(1 + C)$ minus the constant term 1, which includes all combinations of $A$, $B$, and $C$ multiplied together. Final answer: $$A + B + C + AB + BC + AC + ABC$$