## Subject (1).

c) Is it possible to divide 5 apples of the same size equally among 6 children in such a way that at least one apple will not be cut into more than 3 pieces? (You are allowed to cut an apple into any number of equal pieces). Justify your answer! ....................................................... 3 points
Solution. Besides the ambiguity between the permission in parentheses and the imposed restriction, the requirement is too weak; we can perform the division so that no apple is cut into more than three pieces, and this in a trivial way, by halving three apples and dividing the other two apples - each into thirds. $\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$ is the mysterious equation (six times) ...