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Annual Harvard-MIT November Tournament

Combinatorics Difficulty 4.4 AIME Find the answer United States

Problem:

Paul starts with the number $19$ . In one step, he can add $1$ to his number, divide his number by $2$ , or divide his number by $3$ . What is the minimum number of steps Paul needs to get to $1$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Answer: $6$

One possible path is $19 \rightarrow 20 \rightarrow 10 \rightarrow 5 \rightarrow 6 \rightarrow 2 \rightarrow 1$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.