When did the constitution change to count enslaved blacks as whole persons?

1868.

Explanation:

The Constitution outlawing slavery was changed in 1865. The 13th and 14th Amendments were the result of the three-fifth compromise agreement. The three-fifth compromise agreement was enacted in the law which gave Southerners more power by counting their slaves to gain taxation and representation.

After the Civil War, the Congress passed 13th, 14th, and 15th Amendments which abolished slavery gave them rights to be called a citizen of the United States, and right to vote. These amendments were passed in the years 1865, 1868, and 1869-70 respectively.

The foundation of counting blacks as a whole person was in 1865 with the 13th Amendment which abolished slavery. But, it was officially enacted with the 14th Amendment which stated that the African-Americans will be counted as a whole person and not 3/5 persons.

So, the correct answer is 1868.