01
Check counts before checking neighbours
One candidate sequence is A, B, A, C, B, C. It contains two occurrences of every label, so it uses the supplied inventory exactly. Read each neighbouring pair in order: A–B, B–A, A–C, C–B and B–C. None has identical labels. This establishes only that the candidate satisfies the stated linear rule. It does not establish that the colours have equal brightness, that garments coordinate, or that text placed on the swatches will be readable. Those are separate questions requiring an actual palette and its intended use.
02
Add the closing pair when the display loops
A repeating carousel or continuous decorative band adds a neighbour that a single row does not have: the last card touches the first. For the candidate, that closing pair is C–A, which also differs. Compare A, B, C, B, C, A. It still contains two of each label and has no identical neighbours within the row, but its closing pair is A–A. The second arrangement therefore meets the linear rule and fails the looping rule. The distinction comes from the presentation format, not a change in the inventory.
03
Use a sequence card as a reusable planning record
Record the palette labels, number available of each label, proposed order, linear neighbour check and whether a closing-pair check is needed. Add the intended medium, such as six editorial spreads or a repeating display. If additional rules arise, write them separately: a lead colour on the first card is different from the no-repeat condition. Preserve rejected arrangements with the specific rule they fail. Once actual colours are selected, review legibility and reproduction separately; a successful symbolic sequence is a planning aid rather than a finished design approval.