5 to 10 digits

[Asimov Pupil]

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

[Insane]

Is it 5429112345?

 

***** = 99945

[Asimov Pupil]

looks right

 

thx

[dan19_83]

i'd be interested in knowing how you derived that.

[Insane]

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.

[Algebracus]

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.