9.1. Five children had ten candies in total. The first said: "I have one candy", the second: "I have two candies", ..., the fifth: "I have five candies". How many of these statements could be false?
Answer. From 1 to 5 statements.

Solution. The total number of "claimed" candies is not equal to ten, so at least one of the statements is false. Examples of candy distribution for the number of false statements given in the answer: 1) $1,2,3,4,0 ; 2) 1,2,3,0,4 ; 3) 1,2,0,0,7 ; 4) 1,0,0,0,9 ; 5) 0,0,0,0,10$.

Comment. Correct solution - 7 points. Proven that at least one of the statements is false - 2 points. 1 point for each example. Points are cumulative. Only the answer is given - 0 points. The problem is not solved or solved incorrectly - 0 points.