Magic Grout Cleaner that REALLY works!

Here's the formula:

7 cups warm water
1/2 cup baking soda
1/3 cup ammonia
1/4 cup vinegar

Now this much liquid didn't even come close to fitting into 
my tiny little spray bottle and it probably won't fit in yours 
either, so here is the recipe halved and quartered.

Halved

3 1/2 cups water
1/4 cup baking soda
2 Tbsp + 2 tsp ammonia
2 Tbsp vinegar

Quartered

1 3/4 cup water
2 Tbsp baking soda
1 Tbsp + 1 tsp ammonia
1 Tbsp vinegar

I used the quartered version for the pics below. I also wrote
the formula on a piece of paper and taped it to the bottle. 
Make sure never to mix bleach with ammonia, you will die or
something...

Here is the method:

First of all, it's not really magic. You have to use your muscles.

Mix the ingredients and give the bottle a good shake.
Spray the grout (I started with 2 tiles at a time) and let the spray sit and absorb a little into the grout. Be generous.
Grab a grout brush, scrub brush, or tile brush and scrub the grout vigorously where the spray has been sitting. Don't get it in your eyes, trust me.

Use a clean damp sponge to wipe each line of grout right after you scrub it to pick up all that dirty liquid, might be handy to keep a bucket of warm water nearby because you'll want to continuously rinse the sponge.
Wow, can you see the difference?

You'll want to mop the whole thing when you're done because the baking soda may leave some white residue. Personally, I mopped and towel dried the floor.

Alternatively you could use toilet bowl cleaner, but it has to be the one that contains bleach.

Works but way more expensive than the recipe above though.