# Maze 2012

Execute the operations in the right order to, starting from initial value 2018 reach the value 2017.
The operations surrounded in red are forbidden :
• to divide by two an odd number,
• execute twice in a row the same elementar operation
That is after "/2 +7", we are not allowed to execute an other "+7" at once, hence "+7 /2" is forbidden.
Last operation can't be "-5" (that is D) because we have to make a final "-5" in the context
Reset restarts from the beginning
Cancel ... cancels the last operation
Reverse executes the inverse operations in the reverse order : from end (2017), the target being 2018
(But they are listed in the direct order)
You have just 13 operations allowed, after that, it's lost...
But you may cancel and get back as you want !

Reverse
 operations (forward, from start)

#### The origin

We have to go from 2011 to 2012 through the following maze

By going through an operation, we execute this operation
It is forbidden to execute twice in a row the same operation (we go through it, and we can't return)
The operations are on integers (>0)

We can see at once that 2011 being odd, we can't divide it by 2, hence the very first operation must be +7
We then reach the center of the maze with value 2018
At the output, we can't have just done the ×3 because 2012 is not an multiple of 3
The very last operation must then be -5 and the last value at center of maze was 2017
Hence the script/game above.

We notice that the previous operation (the last in the game) can't be "D = ×3 -5", because followed by the final "-5" would be illegal.
Also the 1st operation can't be "B = +7 /2" because of the initial "+7" (however 2018 is even !)
It is also forbidden to chain "B = +7 /2" after some "A = /2 + 7" because that would be two "+7" in a row etc.
These conditions about parity and chaining greatly reduce the tree of all possibilities !
Nevertheless, without some method, this tree is still too wide to fully explore by hand
You must think more !
Hint : explore also from the end ("reverse" button)
A note pad allows to store the current status (op list and value)