# Mathmatical poser



## CluelessUser (Jan 30, 2007)

My lovely mother has just e-mailed me a lovely little mathmatical poser which has been wrecking my head for the last couple of hours and I still have no idea what the solution is.

*4/6=4    Add 2 digits which must be the same number to make this equation work*

You're not allowed to add anything other than 2 digits which must be the same number. i.e you can't add in a + - / = * etc.

Someone intelligent help me out please.   

I'll let you know if I get the answer by any other means.


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## Oorang (Jan 30, 2007)

When they say "add" do they mean perform addition, or concatenate? That is:
 4+19 = 23 
23+1 = 24
24/6=4

Or are they looking for you to actually concate 2 digits to any segment of the equation?

I am pretty sure that is it.... Unless I goofed the code. Look:
	
	
	
	
	
	



```
Sub FindSolution()
Dim x As Byte
Dim y As Byte
Dim n As Integer
For x = 0 To 9
For y = 0 To 9
    n = x & y & 4
    If n / 6 = 4 Then MsgBox n
Next y
Next x
For x = 0 To 9
For y = 0 To 9
    n = x & y & 6
    If 4 / n = 4 Then MsgBox n
Next y
Next x
For x = 0 To 9
For y = 0 To 9
    n = x & y & 6
    If 4 / 6 = n Then MsgBox n
Next y
Next x
End Sub
```
The only thing this finds is 24. So if it is concatenetation then the it's 024.


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## CluelessUser (Jan 30, 2007)

This isn't an Excel related puzzle so it has nothing to do with concatenating numbers. I only posted this on this forum because I know you lot are intelligent and good with numbers.

The question is asking you to insert 2 of the same digits in to the formula

For example.....  4/6=4 could become 24/6=42 (Which is incorrect but it shows the right thinking)


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## Oorang (Jan 30, 2007)

Then as the code demonstrates... There is no possible solution if you cannot add operators or use leading zeros.


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## Oaktree (Jan 30, 2007)

I have the feeling it's something like =4/16=1/4 and the person gave you the instructions wrong, as it requires the extra "/"


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## CluelessUser (Jan 30, 2007)

I am assured there is a solution. I have do idea what it is though.

I've tried thinking outside the box but it's too bloody cold out there.


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## Oorang (Jan 30, 2007)

Wait my proof is not exhaustive... hang on a sec will post back.


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## CluelessUser (Jan 30, 2007)

> Wait my proof is not exhaustive...


Well you are certainly right there.

I have just been given the answer. It is actually quite simple when you know the answer.

I have written the answer below in WHITE text so for anyone that wants more time to try and work it out for themselves they can't see it. If you do want to know then highlight the text to be able to see it.

Answer is between here.....

4*<sup>4</sup>*/6*4*=4........ That's 4 to the power of 4 divided by 64 equals 4

....and here.


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## Oorang (Jan 30, 2007)

This breaks the rule of your original post! You said:


> You're not allowed to add anything other than 2 digits which must be the same number. i.e you can't add in a + - / = * etc.



And by those rules there is not solution... And here is proof:

```
Sub Test()
Dim x As Byte, y As Byte
Dim n As Integer
For x = 0 To 9: For y = 0 To 9
    n = x & y & 4:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = y & x & 4:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = 4 & y & x:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = 4 & x & y:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = y & 4 & x:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = x & 4 & y:    If 4 / 6 = n Or n / 6 = 4 Then MsgBox n
    n = x & y & 6:    If 4 / n = 4 Then MsgBox n
    n = y & x & 6:    If 4 / n = 4 Then MsgBox n
    n = 6 & y & x:    If 4 / n = 4 Then MsgBox n
    n = 6 & x & y:    If 4 / n = 4 Then MsgBox n
    n = y & 6 & x:    If 4 / n = 4 Then MsgBox n
    n = x & 6 & y:    If 4 / n = 4 Then MsgBox n
Next y: Next x
End Sub
```


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## CluelessUser (Jan 30, 2007)

Firstly, I didn't create the question or the answer, I just posted it on here looking for some help so please don't shoot the messenger.

Secondly, I think the answer does fit within the rules, it adds 2 of the same number to the original equation to create a correct result.


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## Oorang (Jan 30, 2007)

Ahh... You're right. I misinterpreted the question  Doh!


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## Oaktree (Jan 30, 2007)

In that case, there is more than 1 solution:

4^4/64 = 4 and 4^1/1^6=4 would both work.


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## CluelessUser (Jan 30, 2007)

> In that case, there is more than 1 solution:
> 
> 4^4/64 = 4 and 4^1/1^6=4 would both work.



The problem with 4^1/1^6=4 is that the 6 is already in the original equation as a regualar 6 and you need to change it to a superscript 6.
Minor detail I admit, but true none the less. Good thinking though.


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## Oaktree (Jan 30, 2007)

Well, if they're going to go that route, the 6 is probably close enough to the = sign to prevent the insertion of the 4 after the 6


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## Greg Truby (Jan 30, 2007)

It's a neat puzzle - one I'd seen before, but it had been long enough ago that I'd forgotten the solution. But it is a bit "sneaky" in that when one says that you cannot insert another operator, the implication is that one cannot insert another _operation_ which leads one to mentally cross using exponentiation from the list of things you can do.


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## Oorang (Jan 30, 2007)

I feels cheap & violated


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