Invariant

7 reasoning problems in this domain. Each starts from a depth archetype and bridges toward a competition type.

Fast sums using pattern and symmetry Sum of Evenly Spaced Numbers via the Middle → Pair-Sum Invariant

Perimeter of a figure built from squares Perimeter by Tracing Every Side → Pair-Sum Invariant

Rectangle side and perimeter from equal squares Tile and Cut Figures with Congruent Pieces → Pair-Sum Invariant

Compute one expression several ways Decompose a Number into Parts and Factors → Arithmetic Expression Decomposition

Simplify long add-subtract chains Sum of Evenly Spaced Numbers via the Middle → Pair-Sum Invariant

Flipped digital clock readings Transformations Preserve Measures → Paper Fold-and-Cut Symmetry

Clock seen in a mirror Transformations Preserve Measures → Paper Fold-and-Cut Symmetry