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We-define-a-domino-as-being-and-ordered-pair-of-distinct-integers-A-suitable-sequence-of-dominos-is-a-list-of-distinct-dominoes-in-which-the-first-coordonate-of-each-pair-after-the-first-is-equal-to-




Question Number 205654 by Lindemann last updated on 26/Mar/24
We define a domino as being and ordered pair of distinct  integers. A suitable sequence of dominos is a list of distinct  dominoes in which the first coordonate of each pair after  the first is equal to the second coordonate of the immediately  preceding pair, and in which the pairs (i;j) and (j;i)  do not both appear for all i and j. Let D_(40)  the  set of all dominoes whose coordonate are not greater  than 40. Find the length of the longest suitable sequence  of dominoes that can be formed using the dominoes of D_(40) .
$${We}\:{define}\:{a}\:{domino}\:{as}\:{being}\:{and}\:{ordered}\:{pair}\:{of}\:{distinct} \\ $$$${integers}.\:{A}\:{suitable}\:{sequence}\:{of}\:{dominos}\:{is}\:{a}\:{list}\:{of}\:{distinct} \\ $$$${dominoes}\:{in}\:{which}\:{the}\:{first}\:{coordonate}\:{of}\:{each}\:{pair}\:{after} \\ $$$${the}\:{first}\:{is}\:{equal}\:{to}\:{the}\:{second}\:{coordonate}\:{of}\:{the}\:{immediately} \\ $$$${preceding}\:{pair},\:{and}\:{in}\:{which}\:{the}\:{pairs}\:\left({i};{j}\right)\:{and}\:\left({j};{i}\right) \\ $$$${do}\:{not}\:{both}\:{appear}\:{for}\:{all}\:{i}\:{and}\:{j}.\:{Let}\:{D}_{\mathrm{40}} \:{the} \\ $$$${set}\:{of}\:{all}\:{dominoes}\:{whose}\:{coordonate}\:{are}\:{not}\:{greater} \\ $$$${than}\:\mathrm{40}.\:{Find}\:{the}\:{length}\:{of}\:{the}\:{longest}\:{suitable}\:{sequence} \\ $$$${of}\:{dominoes}\:{that}\:{can}\:{be}\:{formed}\:{using}\:{the}\:{dominoes}\:{of}\:{D}_{\mathrm{40}} . \\ $$

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