M2S3: From 11 to 25

Logic Level 3

In the game of M2S3, the goal is to use minimum number of steps to get from one number to the next. In each step, you can either

• multiply by 2, or
• subtract 3.

For example, if we wanted to get from 8 to 11, we could do so in 5 steps:

$\large 8 \overset{-3}{\longrightarrow} 5 \overset{\times2}{\longrightarrow}10 \overset{-3}{\longrightarrow} 7\overset{\times2}{\longrightarrow}14 \overset{-3}{\longrightarrow}11.$

What is the minimum possible number of steps required to get from 11 to 25?

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