# Happy Math

1. Feb 27, 2005

### T@P

26/65 = 2/5 (cross out the sixes)

16/64 = 1/4 (again cross out the sixes)

are there anymore *interesting* numbers like this?

by interesting i mean that its not 11/11, since you can obviously cross out the 1's and get 1/1. the numbers have to be different

also, are there any 3 digit ones where you can cross out 2 of the digits? (etc, etc)

2. Feb 28, 2005

### Alkatran

Program:
Code (Text):

Dim x As Single
Dim z As Single
Dim y As Single
For x = 1 To 1000
For z = 1 To 1000
If 10 * x / z <> 1 Then
y = 9 * x / (10 * x / z - 1)
If y = CLng(y) And y > 0 And (y <> x Or y <> z) Then
If CSng(x & y) / CSng(y & z) = x / z Then
Debug.Print x & ", " & z & ", " & y & ": " & x & y & "/" & y & z & "=" & x & "/" & z
End If
End If
End If
Next z
Next x
End Sub

Results:
1, 4, 6: 16/64=1/4
1, 5, 9: 19/95=1/5
2, 5, 6: 26/65=2/5
4, 8, 9: 49/98=4/8

There are no 3 digit non-trivial (x=y=z) cases (at least for x and z, possibly for y).

3. Feb 28, 2005

### T@P

thanks alot for all the help. :)