Candy bars Beeblebrox has a candy bar with n squares. The candy bar is in the shape of an n × 1 rectangle, with n – 1 grooves betwcen the squares. Beeblebrox wants to break the candy bar into n squares, by breaking a piece along one of its grooves. Each break takes a picce of k squares and breaks it into two picces, one picce consisting of a squares and a second picce consisting of the remaining k – a squares, for some 0 < a < k. Beeblebrox uses exactly n – 1 breaks in total. This is though a game, and Beeblebrox carns points cach time he breaks a picce, and Beeblebrox wants to carn as many points as possible. If Beeblebrox breaks a picce of k squares into two picces of a and k – a squares, then Beeblebrox carns max{a, k – a} points. (max{r,y} = x if x > y, and otherwise max{r, y} = y.) 1. Suppose that Beeblebrox applies the following strategy T: (1) Repeatedly, n – 1 times, he takes the remaining candy bar and break off exactly one piece. Let T(n) denote the total number of points that Beeblebrox carns, if he starts with a candy bar with n squares. Then we can formulate a recurrence that measures the total number of points Beeblebrox carns: T(n) = (n – 1) +T(n – 1) for n > 1, and T(1) = 0. Give a closed form for this recurrence, and briefly justify your answer. (No proof is required.)

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