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As for the other hints given: "lives in California near the 100th street" - Californium has atomic number 98. "Today he decided to take his palindromic boat" - Googling this turns up "kayak". Dunno what to do with that. "and visit France. He booked a room which has a number of thrice a prime." - Francium has atomic number 87 = 3 * 29.
>! So drink from 11, walk to 10 9 8 (but not to 7 because at this point it's empty); drink from 8, walk to 9 8 7 6; drink from 6, walk to 7 6 5 4; drink from 4, walk to 5 4 3 2. Ah yes, so there is a minor mistake there; the cow needs to drink from 2, walk to 3 2 1, and it's done.
What arithmetic problems are there? The problem statement requires some interpretation, but that answer seems to be a reasonable way to interpret it. >! Assumption: "This repeats on the 3rd and 4th drinks, and so on" means that they each repeat the 2nd (go back one before going forward). So drink from 1, walk to 2 3 4 5; drink from 5, walk to 4 5 6 7; drink from 7, walk to 6 7 8 9; drink from 9, walk to 8 9 10 11. >! Assumption: Now the first walk toward 1 is 100% forward, and each subsequent walk takes one step back toward 11 before continuing forward toward 1. (continued next comment)
In base 3, the weights are 1, 10, 100. Consider the state where all of them are on the left. Now how much can you increase the difference between right and left? Removing a weight increases the difference by the amount of that weight. Moving a weight to the right increases the difference by twice the amount of that weight. So the possible differences are 000, 001, 002, 010, 011, 012, ..., 222 (or, returning to base 10, 0 through 26). And the initial difference was -13, so the full set of differences is -13 through +13.
