The solvability of a set partitioning problem and a logical mistake in article 2 of the U.S. Constitution

An elementary proof of the solvability of a set partitioning problem of a special kind is presented. The solvability of this problem, in particular, means that a requirement from Article 2 of the U.S. Constitution might not be met in U.S. Presidential elections held under the double-balloting principle of casting the electoral votes by the Electoral College when the number of all the appointed electors was even.