In this XKCD comic, a stick figure asks an NP-complete problem to order exactly 15.05 worth of appetizers out of a menu that includes the following list of prices: {2.15, 2.75, 3.35, 3.55, 4.20, 5.80}.
What is the mathematical name and procedure for this kind of problem, and how would you input something like this to WolframAlpha if possible?
To count the number of solutions, enter
series for 1/((1-x^(215/100))(1-x^(275/100))(1-x^(335/100))(1-x^(355/100))(1-x^(420/100))(1-x^(580/100))) at x=0(or click here), then press "More Terms" about two dozen times until you get the coefficient for $x^{1505/100}=x^{301/20}$, which is $2$, so there are two solutions.For a slightly smaller problem, you could also get the solutions themselves by entering
series for 1/((1-a x^(215/100))(1-b x^(275/100))(1-c x^(335/100))(1-d x^(355/100))(1-e x^(420/100))(1-f x^(580/100))) at x=0(or clicking here) and decoding the coefficient of $x^{1505/100}$. Unfortunately Wolfram|Alpha stops offering more terms at $x^{10}$, so the best we can do is to deduce from the coefficient $a^3d+ef$ of $x^{10}$ that there are two appetizer combinations for exactly $\$10$, namely $3$ mixed fruit and hot wings, or Mozzarella sticks and a sampler plate.To see why this works, you can read up on the generating function for the partition function.