# IQ Sort

Computer Science Level 5

In a remedial math class, the teacher decides to seat the students in an IQ order. The seats are setup in a way that they appear in a horizontal line.

The order is such that when a hypothetical person X is to the left of a hypothetical person Y, and X is not more than 8 IQ points higher than Y.

For Example, Say that in the math class, there are five students that have IQs of $$60, 65, 70, 75, 80$$. The students could be put in an order of $$60, 70, 65, 80, 75$$.

If the class had 20 students with IQ scores: 20, 25, 30, 35, 40, 45, 50, 55, 60, 64, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, in how many ways could the students be seated in the order defined above?

Note:

• There is someone of IQ 64.
• This problem can also be solved using a computer.
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