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Probability Level 5

N N non-zero real numbers ( N ≥ 2 ) (N \geq 2) are written on a board. Calvin erases any two numbers, say a and b, and then writes the numbers A + B 2 A + \frac{B}{2} and B − A 2 B - \frac{A}{2} instead. Then which of the following is true:

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After 2 n + 3 2n + 3 operations, the set of numbers on the board coincides with the initial set After any number of operations, the set of numbers on the board can't coincide with the initial set After a finite number of operations, the set of numbers on the board coincides with the initial set After 3 n + 2 3n + 2 operations, the set of numbers on the board coincides with the initial set

Vatsalya Tandon by Vatsalya Tandon , 21, India

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