## Subject (1).

b) Fill in the free cell in Line 1 with the appropriate number so that the numbers written in this line follow the rule according to which the other three lines are filled. ......................................................... 3 points

| Line 1 | 5 | 8 | $?$ | 6 |
| :--- | :---: | :---: | :---: | :---: |
| Line 2 | 16 | 20 | 14 | 12 |
| Line 3 | 34 | 25 | 18 | 16 |
| Line 4 | 20 | 28 | 45 | 31 |
Solution. There is no solution! Or, if you want, the intended solution is probably to "observe" that the sum of the numbers in Line k is $31k$, with $2 \leq k \leq 4$; then the missing element in Line 1 will be $31-(5+8+6)=12$. But unfortunately, there are infinitely many conceivable "rules" - choosing the one above is an application of "Occam's razor" (among multiple possibilities, go with the "simplest"). In the end, the lines have more of a property than a rule by which they were formed. This type of question is more suitable for almanacs, or recreational mathematics sections, than a school competition; inappropriate skills should be avoided, especially coming from an "educational authority."