Cooling The Wort

If this is a ridiculous question, please excuse me, but I was wondering if one could assist their wort cooling by adding water to it instead of just cooling the brew pot in ice (I don't have a wort chiller)? So, if I boiled my batch with 3 gallons of water, could I raise it up to 5-gallons by adding water to the hot wort rather than the already cooled wort in the carboy? Is that even a possibility? I assume there is a reason why one is not told to do this, but I was wondering what it is.

I do this all the time. I still chill my wort by cooling the brewpot in the sink with some ice, but I finish the cooling by topping up with chilled water.

I don't think there is any difference. Heat is energy, and you need to transfer it regardless of the actual temperature. I read somewhere at this forum, though, that some people freeze their top water, and then just drop this block of ice into the hot wort, which is, of course, different.

Absolutely, amen. You can put your 1g jugs in the fridge the day before the brew or freeze it in blocks and this will help your cooling tremendously

You could always freeze a gallon just (filled about 3/4 of the way), cut it apart to get the ice out, then toss it in. Ideally you'd just buy a jug of distilled at the store, pour yourself a glass to drink, then freeze it the day before brewday. Clean and easy for less than a dollar.

You absolutely can, and freezing is better, just keep two things in mind:
A. if you are using tap water, it is not sanitary. I've heard different opinions as to how much difference that actually makes, but it's a point to ponder. Tap water is also chlorinated, which can effect flavor. You can avoid both of these issues if you pre-boil your water, and freeze it in a sanitized container until use. But of course, it's more hassle.
B. You will need more water than you think, half the volume wont do it. I'll demonstrate this: Let's say you have 2.5 Gallons of boiling water (212 deg) and 2.5 gal of ice (32 deg) together you have 5 gal of water in a temp of (212+32)/2 =122<-This is the average temp. Too high. In order to get down to around 70 you'd need about 4 gal of ice to one gal of wort (212*.2 +32*.8=67. figure that wort boils a little hotter than water, so you're probably looking at around 69)
Now in reality that's not exactly true, because the wort losses the first 30 degrees or so in the two minutes after you turn off the heat, and another 10-20 degrees when you pour it into the fermentor. But still, I'd go with at least a 2/3 to 3/4 wort to ice ratio, and even then be prepared for it to be a bit hotter than you'd think

https://www.homebrewtalk.com/f36/ag-adding-water-after-boil-274052/index3.html

Look at the above thread.

I normally buy a bunch of bags of ice to cool my brew pot in my kitchen sink. What about just getting an extra bag and pouring it into the cooling wort? I would, of course, make sure I do not add too much. Any possible problems with that?