Solution to Question 1: I attempted this problem by using Venn diagrams, to initially find the number of medals that Italy must have had, and then simply worked backwards logically to find the number of medals of every type that every other country must have had. We make a Venn diagram with three different sets; Bronze, Silver and Gold (B,S,G). We know that Italy had 27 medals in total, so 27 ∈ B,S,G. We also know that Italy had two more bronze medals than they had gold medals, therefore, assuming that Italy has 9 silver medals (because the lowest number of silver medals that any nation had was 6, and Italy had 3 more than Japan, which had the fewest), we have now 18 medals left between bronze and gold. Therefore Italy must have 10 ∈ B, and 8 ∈ G.
We can now use the fact that Japan has one more Gold medal than Italy to state that Japan has 9 Gold medals. As I said previously, we also know that Japan must have 6 silver medals as we can deduce that it has the fewest since it has "3 fewer silver medals than Italy" and France has "twice as many silver medals as Italy has gold medals". Now, we know that the three nations have 38 bronze medals in total, therefore Japan has 38 - 10 - 18 = 10 Bronze medals.
Finally, we already know that France has 18 Bronze medals and 7 Gold medals from the statements therefore, we can easily its number of silver medals: "France has twice as many silver medals as Italy has gold medals", therefore France has 16 silver medals.
We end up with the logical conclusions in the following table:
Italy: 10 Bronze, 9 Silver, 8 Gold
Japan: 10 Bronze, 6 Silver, 9 Gold
France: 18 Bronze, 16 Silver, 7 Gold