Asimov Pupil Posted April 27, 2005 Share Posted April 27, 2005 the number 54321 is multiplied by a five digit number(*****). the product is a 10 digit number ending in 12345. what is the number we are multiplying by? find what is the astericks Link to comment Share on other sites More sharing options...
Insane Posted April 27, 2005 Share Posted April 27, 2005 Is it 5429112345? ***** = 99945 Link to comment Share on other sites More sharing options...
Asimov Pupil Posted April 27, 2005 Author Share Posted April 27, 2005 looks right thx Link to comment Share on other sites More sharing options...
dan19_83 Posted April 27, 2005 Share Posted April 27, 2005 i'd be interested in knowing how you derived that. Link to comment Share on other sites More sharing options...
Insane Posted April 27, 2005 Share Posted April 27, 2005 It was quite easy: Private Sub Timer1_Timer()Label1.Caption = 54321 * Text1.Text If InStr(Label1.Caption, "12345") Then List1.AddItem (Label1.Caption) End If Text1.Text = Text1.Text + 1 End Sub Simple program I cooked up. Link to comment Share on other sites More sharing options...
Algebracus Posted April 28, 2005 Share Posted April 28, 2005 Another approach is to try to derive the digits by the following method: 54321*abcde=.....12345. e must be 5, since 1*e should end in 5. Now, we have 54321*abcd5 ........271605 ...... Next, d should be 4, since 1*d should end in 4: 54321*abc45 ........271605 ......217284 or in abbreviate form 54321*abc45 ......2444445 Next, 1*c+4 should end in 3, giving c = 9, and then 54321*ab945 ......2444445 ....488889 or 54321*ab945 ....51333345 We now need another 9, so that b + 3 ends in 2, and get 54321*a9945 ....51333345 ..488889 or 54321*a9945 ..540222345 And at last, a = 9: 54321*99945 ..540222345 488889 5429112345 The method will work in all cases (if you substitute 12345 and 54321 with whatever you want), but in this case the method is especially well-applicable, since 54321 ends in 1, and we therefore don't need to check multiple possibilities. Link to comment Share on other sites More sharing options...
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