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Question Number 18655 by Tinkutara last updated on 26/Jul/17

$$\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{odd}\mathrm{integers}$$$$\mathrm{between}30,000\mathrm{and}80,000\mathrm{in}\mathrm{which}\mathrm{no}$$$$\mathrm{digit}\mathrm{is}\mathrm{repeated}.$$

Commented by mrW1 last updated on 27/Jul/17

$${\mathrm{let}}^{\prime }\mathrm{s}\mathrm{say}\mathrm{the}\mathrm{number}\mathrm{is}\mathrm{XZZZY}$$$$\mathrm{X}\mathrm{can}\mathrm{be}3,4,5,6,7$$$$\mathrm{Y}\mathrm{can}\mathrm{be}1,3,5,7,9$$$$\mathrm{Z}\mathrm{can}\mathrm{be}0,1,2,3,4,5,6,7,8,9$$$$\mathrm{case}1:$$$$\mathrm{Y}\mathrm{is}\mathrm{one}\mathrm{from}3\mathrm{digits}\mathrm{in}\{3,5,7\}$$$$\mathrm{X}\mathrm{can}\mathrm{be}\mathrm{one}\mathrm{from}4\mathrm{digits}:4,6\mathrm{and}2\mathrm{from}\{3,5,7\}$$$$\mathrm{ZZZ}\mathrm{can}\mathrm{be}\mathrm{choosen}\mathrm{from}8\mathrm{digits}$$$$\Rightarrow 3\times 4\times 8\times 7\times 6$$$$\mathrm{case}2:$$$$\mathrm{Y}\mathrm{is}\mathrm{one}\mathrm{from}2\mathrm{digits}\mathrm{in}\{1,9\}$$$$\mathrm{X}\mathrm{can}\mathrm{be}\mathrm{one}\mathrm{from}5\mathrm{digits}\mathrm{in}[3,7]$$$$\mathrm{ZZZ}\mathrm{can}\mathrm{be}\mathrm{choosen}\mathrm{from}8\mathrm{digits}$$$$\Rightarrow 2\times 5\times 8\times 7\times 6$$$$$$$$\mathrm{totally}$$$$\Rightarrow 3\times 4\times 8\times 7\times 6+2\times 5\times 8\times 7\times 6=7392$$

Commented by mrW1 last updated on 27/Jul/17

$$3\times 4\times 8\times 7\times 6+2\times 5\times 8\times 7\times 6=7392$$

Commented by Tinkutara last updated on 27/Jul/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{mrW}1\mathrm{Sir}!$$

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