How many different phenotypes can be produced by a pair of codominant alleles?

Three

Explanation:

Codominant alleles are those alleles that when ars togehter in the genotype (heterozygous) are  expressed simultaneously. An example of codominant alleles are  those for the AB blood types: when allele for A and allele for B are together in heterozygous, both are expressed in phenotype. Another two possible phenotypes produced by this pair of codominant alleles are  A blood type (when two A alleles are in homozygous genotype) and B blood type (when two B alleles are in homozygous genotype).

that scientist would be robert hooke