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This problem trains for: SAT-I, AMC-8, GMAT.

Beeblebrox is frantically looking for the code that will start the teleporter. The emergency instructions read: "input the 279-th number in the sequence: 1, 3, 5, 7, 9, 7, 5, 3, ... where all odd numbers from 1 to 9 are repeatedly listed forward and backward." The mainframe computer is on strike and the little pocket calculators have black-on-black displays. What number must Zaphod put in?

(characters inspired from Douglas Adams' "The Hitchhiker's Guide to the Galaxy")

The sequence has a period that is 7 numbers long:

equation

Compute the remainder when dividing 279 by 7:

equation

The remainder is 6. The number that must be input is the 6-th number in the period. Therefore, it is the number 5.