Here is the question:
Rulerette. Suppose in the game Ruler, we are not allowed to turn over just one coin. The rules are: Turn over any consecutive set of coins with at least two coins being turned over, and the rightmost coin going from heads to tails. Find the Sprague-Grundy function for this game and relate it to the Sprague-Grundy function for Ruler.
So I understand what I'm suppose to be doing but when I do the calculations I am not getting the answer the book has written out. So I want to figure out what exactly I am doing wrong.
Here is what I am doing.
since the rule states that i need to turn over at least two coins,
g(x) = mex {g(x-1)+ g(x-2), g(x-1)+...+g(1)}
the + represents binary operation. What I'm getting stuck on is number 4 and 6.
working it out I get the following:
g(4) = mex{g(3)+g(2) = 0 +1 =1, g(3)+g(2)+g(1)= 0 + 1 + 0 = 1} so it should be 0, right?
but the table says 2. which I'm so confused about. Any help would be GREAT