Um... is this a solution? Let the 100 jars have $ a_1, a_2, ...., a_{100} $ amounts of jam respectively on the first day. Then If Karlsson eats $min\{a_1, a_2,...,a_{100}\} $ he will succeed in emptying atleast one jar. By following a similar strategy he can eventually eat up all the jam.

AdithyaBhaskar wrote: Um... is this a solution? Let the 100 jars have $ a_1, a_2, ...., a_{100} $ amounts of jam respectively on the first day. Then If Karlsson eats $min\{a_1, a_2,...,a_{100}\} $ he will succeed in emptying atleast one jar. By following a similar strategy he can eventually eat up all the jam. You probably misread the problem: It's said that there are 1000 jars (not 100 as your post suggests)... Anyway, your solution would have been astoudingly simple for such kind of problem.

Actually if there were 100 jars this solution would be wrong because if you empty one of the jars, you can no longer eat anything from it.