The Survivor There are 13 contestants on a reality television show. They are instructed to each take a seat at a circular table containing 13 chairs that are numbered consecutively with the numbers 1 through 13. The producer then starts at number 1 and tells that contestant that he is a survivor. That contestant then leaves the table. The producer skips a contestant and tells the contestant in chair number 3 that he is a survivor. That contestant then leaves the table. The producer continues around the table skipping a contestant and telling the next contestant that he is a survivor. Each survivor leaves the table. The last person left at the table is not a survivor and must leave the show.
a. For n = 13 find the unlucky number k, for which the person sitting in chair k must leave the show.
b. Find k for n = 8, 16, and 41.
c. Find a formula for k.
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