What would be the transition for ten coins?

Question

• There are ten coins
• and a move is made up of flipping any three adjacent coins:
• H H T T H T H T H T -> H T H H H T H T H T (flip: 2,3,4).
• How can this transition be represented?
• /
• EG: There are 102 coins (98H, 4T)
• Transitions are : 1) Flip over any 10 coins
• 2) if there are n heads, add (n+1 )tails. is represented as
• 1) h'=h+10−2m and t'=t−10+2m, where m=[0-10] - flipping m heads and 10-m tails
• 2) h'=h and t'= t+h+1 (add h+1 tails)
• /

• How can I define the transition of flipping three adjacent coins?

• Thanks in advance

Answer 1

Try considering the coins in positions 1,2,4,5,7,8, and 10 (i.e. positions not divisible by 3) and find a pre-served invariant of this system.