Something strange regarding carbon 14 in the Great Pyramid

Question

The Great Pyramid at Giza was carbon dated using charcoal found in the mortar between the stones. As the scientists wanted to see how long it took to build, samples were taken from the base, and from the top. Upon testing, they did find about 100 years difference in the readings. The problem was, that the top came out older than the bottom ?????

What went wrong - or how can we account for this ?

I'll give a few theories of my own -

The pyramids were built from the top down (unlikely)

They only were using trees 100 years older when building the top.

Weathering of the top material

Bombardment of Cosmic radiation more likely at the top.

The pyramid contained a radioactive source at some point (hence all the warnings and curses)

Answer 1

I like the cosmic radiation theory.  We are only talking about parts per trillion difference in concentration or some really small amount.  The greater exposure at the top should be able to shift it a little compared to the bottom over such vast time frames.

Answer 2

Do you have a link to this study?  I have read items online regarding dating issues in the Pyramids, but never an analysis that suggested different heights had different ages.  Narrowing down the data to such small time frames is generally not possible, so this surprises me.