Melody

Thanks jfan17,

That is the exact one I was looking for.   

Hopefully I will post my answer today.

Thanks   CalTheGreat, 

I could not remember who posted it otherwise I would have done that.

Also, I did not remember that I had responded or else I might have found it that way.

Hi TR it is good that you are back :)

Not a bad idea TR. But rather than burn it why don't you just store it for them ( maybe in your stomach)?

I have played with it but I have not gotten very far. 

Attn: CalTheGreat

There is only one side 

This is NOT an equation.

All you are being asked is, 'what number do you need to add to   x^2 +22x    in order to make the expression a perfect square'.

the answer is   \((\frac{22}{2})^2 = 11^2 = 121\)

\(x^2+22x+\boxed{121} = (x+11)^2\)

Does anyone have the ability to check these answers?

I think it can be done in Wolfram|Alpha but I do not know how to phrase the question to get the answer......

Thanks for pointing this old post out guest. :)

I have linked it to this one. 

Continued here:

Hi jfan17,

I am not brilliant or infallible on these counting questions either but I cannot follow your logic.

This is what I think.

Choose one of the beads to be a marker. It does not matter which one but I think the logic is easier to follow if you chose one of the individual ones. I will call it bead X

Now there are 5 beads left to place and one is a repeat so I think that will be  5!/2! = 60 permutations.

So far I have accounted for rotations being the same but I have not accounted for reflections.

The X bead is fixed.  There is only one axis of symmetry that allows this bead to keep the same position.

One reflection line makes two halves so I must divide by 2.

So I think that the answer is 30 possibilities.