A man is walking along a numbered path. He repeats the following process of taking 10 steps forward and N steps backward. What should N be in order to guarantee at least one number along the path will be stepped on exactly 5 times. This includes a forward and backward step adding to the total. A tile must be stepped onto to count and not simply stepped off  Options:
A) 1	B) 2	C) 3	D) 5	E) 6
Assuming the man's overall direction is headed forward is forward from no answers being greater than 10   Actions:   1: 10 steps   2: 10 - N steps   3: 20 - N steps   4: 20 - 2N steps   5: 30 - 2N steps   6: 30 - 3N steps   All answers less than or equal to 5 are out since by the 4th action the number tile will be 10. Following the procedure, N=5 will making every tile less than 10 have 3 or fewer steps.   N=6 will allow the 4th action to be 8 making it the first number readily breach single digits for the starting action. This is an important thing to notice since hitting tiles reached by the first action will allow the greatest amount of countable steps.   Steps by the end of the 5th action   7: 3 steps   8: 3 steps (stepped off from)   9:5 steps   10: 4 steps   11: 3 steps   12: 3 steps   By the 6th action, the steps will be at 12 an won't making it back to any tile 1-10. Since this is repeating, inferring that after every 6 actions the process is a renewable position making tile 9 the only tile with 5 steps other than every other tile after that limiting it to 5 steps.   6 is correct
<result>E</result>
A man is walking along a numbered path. He repeats the following process of taking 10 steps forward and N steps backward. What should N be in order to guarantee at least one number along the path will be stepped on exactly 5 times. This includes a forward and backward step adding to the total. A tile must be stepped onto to count and not simply stepped off