  In this paper we consider ordinal sums of combinatorial games where each
summand is a number, not necessarily in canonical form. In doing so we give
formulas for the value of an ordinal sum of numbers where the literal form of
the base has certain properties. These formulas include a closed form of the
value of any ordinal sum of numbers where the base is in canonical form. Our
work employs a recent result of Clow which gives a criteria for an ordinal sum
G : K = H : K when G and H do not have the same literal form, as well as
expanding this theory with the introduction of new notation, a novel ruleset,
Teetering Towers, and a novel construction of the canonical forms of numbers in
Teetering Towers. In doing so, we resolve the problem of determining the value
of an ordinal sum of numbers in all but a few cases appearing in Conway's On
Numbers and Games; thus generalizing a number of existing results and
techniques including Berlekamp' sign rule, van Roode's signed binary number
method, and recent work by Carvalho, Huggan, Nowakowski, and Pereira dos
Santos. We conclude with a list of open problems related to our results.
