6.1. In a large greed pill, there are 11 g of antimatter, in a medium pill -1.1 g, and in a small pill -0.11 g. The doctor prescribed Robin-Bobin to consume exactly 20.13 g of antimatter. Can Robin-Bobin follow the doctor's prescription by eating at least one pill of each type? (If he can, explain how; if not, explain why.)
Answer: will be able to.

Solution. Let's list all possible examples of sets of pills.

1) 1 large, 1 medium, 73 small; 2) 1 large, 2 medium, 63 small;
2) 1 large, 3 medium, 53 small; 4) 1 large, 4 medium, 43 small;
3) 1 large, 5 medium, 33 small; 6) 1 large, 6 medium, 23 small;
4) 1 large, 7 medium, 13 small; 8) 1 large, 8 medium, 3 small.

Let's explain why there are no other examples. By trying one pill of each type, Robin-Bobin will consume $11+1.1+0.11=12.21$ g of antistuff. Additionally, he will need to consume $20.13-12.21=$ $=7.92$ g of antistuff. Robin-Bobin will not be able to consume more large pills, as $11>7.92$. However, he can consume any number of medium pills from zero to seven.

# Evaluation criteria:

+ one or several correct examples with explanations (calculations) are provided

$\pm$ one or several correct examples without explanations (calculations) are provided

$\mp$ the correct answer "will be able to" and reasonable considerations are provided, but an error is made, resulting in an incorrect example

- only the answer is provided (example is missing)