📐 Gauss 7 Contest Prep

Factor trees · GCD/LCM · divisibility rules · divisor counting

Prime factorization is the single highest-frequency Gauss tool. Builds factor trees, divisibility tests, GCD/LCM via prime factorization, and the divisor-counting application.

%-of-% chains · circle graphs · the complement trick

Beyond textbook fraction-decimal-percent: chained percentages, circle graphs, and "one-minus" complement reasoning.

a:b setup · before/after manipulation · d = rt · mixtures

Ratios manipulated after an event; unit-rate algebra (distance/speed/time); money and mixture problems with a clean variable setup.

Let x = … · one-variable equations · letters as digits

Front-loads Grade 7 algebra: translate words → variable, solve, then graduate to cryptarithms — Gauss's recurring digit-puzzle flavor.

Angle sum · vertical & parallel · isosceles chains

Angle chasing: triangle sum 180°, straight & vertical, parallel-line theorems, and isosceles "two-sides-equal-two-angles-equal" chains.

Composite areas · shaded regions · k → k² → k³

Areas of composite shapes, shaded-region casework, and the scaling law that wins Part B: length k → area k² → volume k³.

Period reduction · arithmetic sequences · mod 7 calendars

nth-term-of-a-repeating-pattern via n mod p; arithmetic-sequence formulas; calendar problems via mod 7.

List · complement · pigeonhole · disjoint cases

The Part-C workhorse: systematic enumeration, complement counting, pigeonhole, casework discipline — and avoiding double-counting.

Weighted outcomes · missing-term mean · optimize under constraints

Weighted/multi-stage probability; mean problems in both directions; median/range constraints with "smallest possible" optimization.

The 2-pt blank rule · pacing · calculator policy · traps

How to actually take the test: blank-vs-guess decision, $\frac{A}{B}$/C pacing, calculator timing, and the four trap families that cost students 20+ points.