How a Scribe Might Have Done It

The guesses for the formulas for triangular and pyramidal numbers used rational fractions. This might have been a little advanced for the scribes of the Pyramid Age who only used unit fractions. The guesses can be rewritten using the four arithmetical operations addition, subtraction, multiplication and whole number division. The notation is a common one used for unit fractions. The Egyptian method for writing numbers was a little more cumbersome that decimal notation. There was a special glyph that represented 2/3rds. The scribes would have had the skills needed to do calculations for following problem. And the need to know the number of blocks required to build a pyramid would have suggested it.