Letter & Number Analogies

At a glance 7 rules

1. 1Letter analogiesLetter analogies are codes with one example: find the change with EJOTY positions, a shift, the mirror $27 - n$ or a reversal, confirm it on every letter, then apply it.
2. 2Copy the letter shiftsIf the letters move by different amounts (+2, +3, +4), copy each place's shift to the new cluster, but only after checking it on every example pair.
3. 3When shifts disagreeIf the example pairs use different shifts, stop copying shifts and test the positions themselves: doubled, squared or mirrored (C to F, E to J is doubling).
4. 4Number pairs: classic linksFor a pair n : m test, in turn, $n^2 \pm 1$, $n^3 \pm n$, $n(n + 1)$ and $\tfrac{n(n - 1)}{2}$ (10 : 45), the next prime (13 : 17), then a fixed $\times k$ or $+k$.
5. 5Check every given pairOne pair fits many rules (3 : 12 is $4n$, $n^2 + 3$ or $n(n + 1)$). Keep only the rule that also fits every other pair you are given.
6. 6Triads: build the middleIn a set like (4, 36, 9), make the middle number from the two ends: the product first, then sums, squares and their differences ($6^2 - 4^2 = 20$).
7. 7Whole numbers onlyWhen the question says not to split numbers into digits, never use digit sums or digit products; work with the whole numbers only.