2. Variant 1.

Nine integers from 1 to 5 are written on the board. It is known that seven of them are not less than 2, six are greater than 2, three are not less than 4, and one is not less than 5. Find the sum of all the numbers.
Answer: 26.

Solution. A number not less than 5 is 5. There is exactly one number 5. Three numbers are not less than 4, so exactly two numbers are equal to 4. Six numbers are greater than 2, meaning all of them are not less than 3. Therefore, exactly three numbers are equal to 3. Seven numbers are not less than 2, so one number is equal to 2. In total, there are 9 numbers, hence two numbers are equal to 1. The sum of all numbers is $1+1+2+3+3+3+4+4+5=26$.