Question Number 120204 by bemath last updated on 30/Oct/20
$${Call}\:{a}\:\mathrm{7}−{digit}\:{telephone}\:{number}\:{d}_{\mathrm{1}} {d}_{\mathrm{2}} {d}_{\mathrm{3}} −{d}_{\mathrm{4}} {d}_{\mathrm{5}} {d}_{\mathrm{6}} {d}_{\mathrm{7}} \\ $$$${memorable}\:{if}\:{the}\:{prefix}\:{sequence}\:{d}_{\mathrm{1}} {d}_{\mathrm{2}} {d}_{\mathrm{3}} \\ $$$${is}\:{exactly}\:{the}\:{same}\:{as}\:{either}\:{of}\:{the}\:{sequences} \\ $$$${d}_{\mathrm{4}} {d}_{\mathrm{5}} {d}_{\mathrm{6}} \:{or}\:{d}_{\mathrm{5}} {d}_{\mathrm{6}} {d}_{\mathrm{7}} \:\left({posibly}\:{both}\right). \\ $$$${Assuming}\:{that}\:{each}\:{d}_{{i}} \:{can}\:{be}\:{any}\:{of}\:{the}\:{ten} \\ $$$${decimal}\:{digits}\:\mathrm{0},\mathrm{1},\mathrm{2},…,\mathrm{9}\:.\:{Find}\:{the}\:{number} \\ $$$${of}\:{different}\:{memorable}\:{telephone} \\ $$$${numbers} \\ $$
Commented by mr W last updated on 01/Nov/20
$$\mathrm{2}×{C}_{\mathrm{3}} ^{\mathrm{10}} ×\mathrm{3}!×\mathrm{7}=\mathrm{10080} \\ $$
Commented by bemath last updated on 01/Nov/20
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$