Partial Mash - Little Calculation Help

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camus

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Playing a bit of guess the OG, should be simple, I can't seem to wrap my head around it.

Back story (long version):

So I thought I would give partial mash brewing a try. Before buying/building anything new I thought I would give Death Brewers method a try.

Any, I mashed 4 lbs of grain in 6 quarts of water as normal. One place I cut a corner is I went and sparged in my kettle, using 4.5 gallons of water. I did this to save some time getting to a boil. After adding the wort to the sparge water I ended up with ~5.25 gallons at 1.020 wort, about what I expected. Then I added water to get to 5.5 gals (about as much as I can currently get to a good boil) and 4 lbs DME. Brought to boil and finished the brew.

I topped off at the end of the boil to get to 5 gallons in the kettle. When I transferred to primary, I tried one of those venturi tube do-hickeys. While checking that out and forgot to take a gravity reading, I usually do this when transferring, got a bit distracted checking out the venturi thing.
So I didn't notice I had left the the test jar empty until I went to take a reading after I had pitched, closed up the bucket and moved it to the basement.


Had a lot fun with this, will definitely be building a mash tun soon, almost did it for this brew, but thought I would try it this way to see how it went.


So now to the question (short version):

I started with 5.25 gallons @ 1.020, added 4 lbs DME (Pilsen Extra Light), ended up with 5 gals.

What should the OG be on this?

Software is telling me it should be 1.055 based on the recipe.
 
I would expect 1.056

My calculation for this:
(5.25 gal x 20 gravity points + 4lbs x 44 gravity points)/5gal
 
And I was at the store picking up some ice melt and oddly left with the parts for a 5 G MLT, I don't even know why I try and fight it anymore.
 
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