Solutions for Session 2, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6

 Problem A1 Some possible answers: each output number is 4 more than the last; the output numbers that appear are all the even numbers that aren't multiples of 4 (starting with 6); the output number is 2 more than 4 times the input number. Also, adding one input to the following input yields half the first output.

 Problem A2 You can't be sure, because the pattern is not completely specified, but it would be likely that the 100th number is 402. This follows the third rule listed above -- that the output number is 2 more than 4 times the input number.

 Problem A3 Again, you can't be completely sure, but it would be likely that the 25th number is 102, because 2 more than 4 times 25 is 102. Following the same pattern, 1004 would not appear in the output column, since 1004 is not 2 more than 4 times any whole number.

 Problem A4 Example: Pick 7, and then follow the algorithm. 7 >> 21 >> 19 >> 38 >> 44 >> 30 is the output. The numbers at the end are the same as the pattern described in the table. Here's why: Pick n instead, which stands for a variable number. Follow the algorithm. n >> 3n >> 3n - 2 >> 6n - 4 >> 6n + 2 >> 4n + 2 is the output, which is the rule described in Problem A1.

Problem A5