+33615 The question is slightly ambiguous. "The same scores" could mean identical scores for each individual problem, or it could mean the same total score. I'll assume the latter.
With 22 problems and the three possible scores of 0, 1 and 3 per problem, the total score could be any of the numbers from 0 to 66. Hence there are 67 possible totals. Therefore we need a minimum of 68 candidates to ensure at least two have the same total score.
