# Maze 2012

#### 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)

Solution