Special Calculator
My calculator is special. It has 2 functions, a x2, and a +3.
The calculator starts with the number 1 everytime I power it on.
I wish to get the number 2016 by using the 2 functions in any order.
What is the least number of steps to get from 1 to 2016?
For example, the least number of steps to get from 1 to 8 is 2. (+3, x2)
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1 solution
It is impossible to get to 2016 since it is impossible to get to any integer divisible by 3. We start with 1, which is not divisible by 3. Adding 3 to an integer that is not divisible by three cannot make it divisible by 3. Similarly, multiplying by 2 cannot make an integer divisible by 3 if it wasn't already.