Teaching-mechanic library

factor_forge · math · builder.tiles

Concept: Factoring

Player does: Arrange algebra tiles into a rectangle whose sides are the factors

Breaks: x² + 5x + 6 = (x + 5)(x + 1)

Factoring requires two numbers that multiply to the constant and add to the middle coefficient, here 2 and 3, giving (x + 2)(x + 3).

area_tiler · math · builder.tiles

Concept: Area vs perimeter

Player does: Tile the room, then fence it; compare both counts

Breaks: More area always means more perimeter

Area and perimeter can change independently, so a shape can have more area with less perimeter, and vice versa.

power_grid_builder · physics · builder.circuit

Concept: Series vs parallel

Player does: Wire the town so every house gets full voltage

Breaks: Adding bulbs in parallel dims all of them

Parallel branches each get the full source voltage, so adding a parallel bulb does not dim the others.

orbital_filling · chemistry · builder.electron_config

Concept: Electron configuration

Player does: Fill orbital slots obeying Aufbau, Hund, and Pauli

Breaks: Orbitals fill in number order (3d before 4s)

The Aufbau principle fills orbitals by increasing energy, which puts 4s below 3d in energy despite the smaller number.

molecule_builder · chemistry · builder.molecule

Concept: Bonding & valence

Player does: Assemble the requested molecule within valence rules

Breaks: Atoms can form any number of bonds

Each element's valence sets a limit on how many bonds it can typically form.

punnett_forge · biology · builder.genetics

Concept: Mendelian genetics

Player does: Fill the Punnett square to breed a familiar with the needed trait

Breaks: Dominant traits are always the most common

A trait's frequency in a population depends on allele frequency, not simply on whether the allele is dominant.

automation_track · cs · builder.program

Concept: Loops

Player does: Configure a repeating action instead of stepping manually

Breaks: A loop checks its condition only once

A loop re-checks its condition every iteration, which is what lets it keep running or stop.

reusable_machines · cs · builder.program

Concept: Functions

Player does: Define a machine once and call it at several stations

Breaks: Functions run when they're defined

A function's body runs only when it is called, not at the moment it is defined.

code_golem · cs · builder.program

Concept: Algorithms

Player does: Program the golem to build the staircase

Breaks: Computers do what you meant

A computer executes exactly what an algorithm specifies, not what its author intended.

logic_factory · engineering · builder.circuit

Concept: Logic gates

Player does: Wire gates so the output matches the target truth table

Breaks: You need AND, OR, and NOT to build any circuit

NAND alone is functionally complete, so every logic circuit can be built from NAND gates without AND, OR, or NOT.

state_explorer · engineering · builder.circuit

Concept: Truth tables

Player does: Test every input combination and fill the table

Breaks: Checking a few inputs proves the circuit

A circuit is verified only by testing every input combination in its truth table, not a sample of them.

grouping_territory · engineering · builder.tiles

Concept: Karnaugh maps

Player does: Cover the 1-cells with the fewest power-of-two rectangles

Breaks: Groups can be any size

Karnaugh map groups must be a power-of-two size (1, 2, 4, 8…) to correctly simplify the expression.

instruction_factory · engineering · builder.tiles

Concept: Pipelining

Player does: Schedule instructions into stages; count total cycles

Breaks: Pipelining makes each instruction faster

Pipelining raises instruction throughput by overlapping stages; it does not shorten any single instruction's latency.

truth_table_logic · philosophy · builder.circuit

Concept: Propositional logic

Player does: Fill the truth table for the compound statement

Breaks: "If P then Q" means "if Q then P"

A conditional and its converse can differ in truth value, so "if P then Q" does not imply "if Q then P".

citation_builder · writing · builder.sentence

Concept: Citation format

Player does: Arrange citation elements in MLA or APA order

Breaks: Every style orders elements the same way

Citation styles like MLA and APA each order and punctuate the same elements differently.

spell_syntax · language · builder.sentence

Concept: Grammar & conjugation

Player does: Cast spells by building correctly conjugated sentences; ElevenLabs voices them back

Breaks: Word order matches English

Word order and agreement rules are specific to each language and often differ from English.

rhythm_bridge · music · builder.tiles

Concept: Meter & note values

Player does: Fill each measure so the note values sum to the time signature

Breaks: A measure can hold any number of beats

A measure's note values must add up to exactly the number of beats set by the time signature.

scale_builder · music · builder.tiles

Concept: Major & minor scales

Player does: Build the scale from the whole/half-step pattern

Breaks: Every scale uses only white keys

A scale is defined by its pattern of whole and half steps, which can require black keys depending on the starting note.

chord_forge · music · builder.tiles

Concept: Triads

Player does: Stack thirds to forge the requested chord

Breaks: Any three notes make a triad

A triad is built by stacking specific thirds on a root, not any arbitrary combination of three notes.