IQ Sort

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?


  • There is someone of IQ 64.
  • This problem can also be solved using a computer.
Thank You, axas bit for sharing this. Shame on you for never replying to my email though.

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