An IQ Mathematics Test has a total of 52 questions with the following rules:
- From questions 1 to 20: 4 points for each correct answer, 1 point deduction is applied to each wrong answer, no points for a blank answer.
- From questions 21 to 35: 5 points for each correct answer, 1.25 point deduction is applied to each wrong answer, no points for a blank answer.
- From questions 36 to 50: 6 points for each correct answer, 1.5 point deduction is applied to each wrong answer, no points for a blank answer.
- Questions 51 and 52: students answer the question and prove the answer, with a maximum score of 20 points per question, no points for a wrong/blank answer. The smallest division of the score is 0.25.
Students who attend the test with no accommodation will be given a base score of 50 points. The minimum score in the test that a test taker can achieve is 0. Given that there are 5 available accommodations students can apply for approval by up to 2 of them:
- With students in a high school (10th grade or higher): no additional score is given.
- With students in a secondary school (grades 6th to 9th): 20×a additional scores is given to the base score, with a is the number of years that the student will be learning in 10th grade.
- With students in a primary school (grades 1st to 5th): wrong answers will receive no penalty. If the student leaves a question with no answer, they will get 25% of the scores in that question. The additional score given to the base score is similar to grade 6th.
- With secondary school students who achieved honorable awards from the International Mathematics Olympiad: the student can skip the first 20 questions, and the scores will be 2 times the maximum score they can achieve from this section.
- With students who are not learning in a primary, secondary or high school: 25 additional scores is given to the base score.
How many possibilities are there for the final score of this test?
