Analogy

high importance~3 Q in Tier 19 formulas⚡ 11 shortcuts6 subtopics

Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.

Letter / letter-cluster analogy

Shift rule

Q(B) = Q(A) + k \pmod{26}

Q = alphabet position; k is constant for a constant-shift analogy.

Opposite letter

Q(B) = 27 - Q(A)

Atbash: A↔Z, M↔N. Two-letter quick check: sum of positions = 27.

Rising shift

Q(B_i) = Q(A_i) + i

Position i gets shift i — common in 4-letter clusters (BDFH from ABCD).

Linear rule

b = k a + r

Solve k and r mentally from a and b; verify on the pair before applying to c.

Square family

b \in \{a^2,\ a^2 \pm r,\ (a{+}1)^2,\ a(a{+}1)\}

Test squares first when b is close to a².

Digit sum rule

b = k \cdot S(a) + r

S(a) = digit sum; common when b is much smaller than a.

Chain rule

b = ka + r,\; c = kb + r

Same step applied twice.

Third from first two

c = ab,\; a^2 + b^2,\; k(a+b)

Test on every model set.

Power set

(a,\; a^2 \pm r,\; a^3 \pm r)

Near-squares and near-cubes.