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MathNet 2008-part-04 — 165 problems (EN–VI) Question 16

Math Olympiad Vault · MathNet 2008-part-04 — 165 problems (EN–VI)

Question 16

Maja can write positive integers onto a blackboard according to two rules. For every number $n$ that is already on the board, she can write down $3n+13$. Whenever one of the numbers on the board is a perfect square, she can also write down its square root.

a. Using only this two rules, can she get the number $55$ assuming she starts with $256$?

b. Using only this two rules, can she get the number $256$ assuming she starts with $55$?