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Pips and tiles, where the arrangement is the notation. Opposite faces of a die have summed to seven since antiquity, a double-six domino set holds twenty-eight tiles because the pairs are unordered, and a mahjong set carries three numbered suits and seven honour tiles that can form sets but never runs. The recurring theme is that the counting rule explains the object: knowing why a domino set is twenty-eight rather than forty-nine is worth more than knowing the number.
The dot patterns on a die, and the rule that opposite faces total seven.
A rectangle split into two halves, each carrying nought to six pips.
Circles, bamboo and characters — three suits numbered one to nine.
Winds and dragons — the tiles with no number and no sequence.