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Question Number 188147 by normans last updated on 26/Feb/23

Answered by Rasheed.Sindhi last updated on 26/Feb/23

$$5\mid ABC\Rightarrow C=0or5$$$$C=0\Rightarrow D=0,4,8[\because 4\mid ABCD]$$$$C=5\Rightarrow D=2,6[\because 4\mid ABCD]$$$$CD=00,04,08,52,56$$$$BCD=000,900,504,108,252,756[\because 9\mid BCD]$$$$B=0\Rightarrow A=3,6,9[\because 6\mid AB]$$$$B=9,5,1,7\Rightarrow Ahasnovalue[\because 6\mid AB]$$$$B=2\Rightarrow A=1,4,7[\because 6\mid AB]$$$$$$$$A=1,3,4,6,7,9$$

Commented by JDamian last updated on 26/Feb/23

$$B\mathrm{and}D\mathrm{are}\mathrm{even}\Rightarrow BCD\notin \{108,504,900\}$$$$C=5\mathrm{because}\mathrm{B}+C+D\mathrm{must}\mathrm{be}\mathrm{either}9\mathrm{or}18$$

Commented by Rasheed.Sindhi last updated on 26/Feb/23

$$Mymistakesir,thankyou!$$

Answered by mr W last updated on 26/Feb/23

$$ithinktherearethreesuchnumbers:$$$$1252,4252,7252$$

Commented by mr W last updated on 26/Feb/23

$$ABCD$$$$B=even,⩽8$$$$C=0or5$$$$B+C+D=9or18$$$$ifC=0:B+D=9\Rightarrow D=odd\Rightarrow rejected$$$$B+D=18\Rightarrow D⩾10\Rightarrow impossible$$$$ifC=5:B+D=4\Rightarrow (B,D)=(0,4)or(4,0)or(2,2)$$$$B+D=13\Rightarrow D=odd\Rightarrow rejected$$$$A054,A450,A252areremaining.$$$$A054:A=6or9\Rightarrow notdivisibleby4\Rightarrow rejected$$$$A450:A=2or5or8\Rightarrow notdivisibleby4\Rightarrow rejected$$$$A252:A=1or4or7\Rightarrow divisibleby4\Rightarrow ok$$$$sothenumberis1252,4252or7252.$$

Answered by manxsol last updated on 26/Feb/23

$$\overline{)\begin{array}{ccccc}A& B& C& D& \\ & & 0& & 5\\ & & 5& & 5\\ & 5& 0& 4& 4,9\\ & 1& 0& 8& 4,9\\ & 9& 0& 0& 4,9\\ & 2& 5& 2& 4,9\\ & 7& 5& 6& 4,9\\ & 2& 5& 2& 6=2\wedge 3\\ 1,4,7& 2& 5& 2& 3\end{array}}$$$$$$

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