Secco and Ramon are drunk in the real line over the integer points a and b, respectively. Our real line is a little bit special, though: the interval (−∞,0) is covered by a sea of lava. Being aware of this fact, and also because they are drunk, they decided to play the following game: initially they choose an integer number k>1 using a fair dice as large as desired, and therefore they start the game. In the first round, each player writes the point h for which it wants to go. After that, they throw a coin: if the result is heads, they go to the desired points; otherwise, they go to the points 2g−h, where g is the point where each of the players were in the precedent round (that is, in the first round g=a for Secco and g=b for Ramon). They repeat this procedure in the other rounds, and the game finishes when some of the player is over a point exactly k times bigger than the other (if both of the player end up in the point 0, the game finishes as well). Determine, in values of k, the initial values a and b such that Secco and Ramon has a winning strategy to finish the game alive. Observation: If any of the players fall in the lave, he dies and both of them lose the game combinatorics proposedcombinatorics