You have been taken prisoner and your captor has set a fiendish problem with which to torture you.
You are stood between two terrible fates. Two steps in front of you is a nest of angry vipers. Two steps behind you is sheer cliff with a drop to certain death. Taking one step forward or back is safe but taking two steps in either direction will be fatal.
Your villainous captor has promised to let you go free if you can write a safe pattern of 12 steps. Unfortunately he will choose whether you follow all the step or every 2nd, 3rd, 4th, 5th or 6th step.
Can you find a pattern that will ensure your release?
- Each step must be forward or back you can not choose to stay still or move in any other direction.
- The sequence must work for all of the following conditions
- all steps 1,2,3,4,5,6,7,8,9,10,11,12 are followed
- only multiples of 2 - steps 2,4,6,8,10,12
- only multiples of 3 - steps 3,6,9,12
- only multiples of 4 - steps 4,8,12
- only multiples of 5 - steps 5 and 10
- only multiples of 6 - steps 6 and 12
The origin of the puzzle is this video https://www.youtube.com/watch?v=pFHsrCNtJu4
(Spoiler warning : the video contains the solution)