Add Math Facts Reaction Duel

[ap0ught]

Feature

Add a synchronized two-player Math Facts Reaction Duel for the paired ESP32-2432S028 CYDs.

Gameplay

• Both players receive the same math fact at the same synchronized start time.
• Each board displays multiple large answer buttons.
• The first confirmed correct answer wins the fact.
• An incorrect answer locks that player out briefly or awards the opponent the point, according to the selected ruleset.
• A match consists of a configurable number of facts, with synchronized scores and a deterministic final winner.
• The result is not final until the submitted answer and reaction event are validated against canonical game state.

Difficulty options

• Addition.
• Subtraction.
• Multiplication.
• Division with whole-number results.
• Mixed operations.
• Configurable operand ranges.
• Optional negative-number and missing-operand modes.
• Optional timed streak mode.

Fair timing

• Precommit each round before revealing the fact.
• Use a synchronized reveal deadline so network arrival order does not determine the winner.
• Record reaction events against the shared round/reveal identity.
• Compare validated reaction timing deterministically with an explicit tie window.
• Reject answers submitted before reveal, after timeout, or for a stale fact.

Synchronization

• Generate facts and answer choices deterministically from synchronized state.
• Guarantee exactly one correct displayed answer and canonicalize distractors.
• Use authenticated sender identity, active-game epochs, ACK/retry, replay rejection, and full-state reconciliation.
• Define behavior for simultaneous correct answers, simultaneous wrong answers, disconnects, and restart recovery.

Navigation

• Both boards provide an EXIT control during countdowns, facts, results, and match completion.
• Either player may return both devices to the shared Home selector.
• EXIT dominates answer events, retries after packet/ACK loss, and cannot be undone by stale packets.

Acceptance criteria

• Facts and answer choices are mathematically valid and deterministic.
• Both boards reveal each fact at the intended synchronized deadline.
• Early, stale, duplicate, wrong, correct, tied, and timed-out answers are handled deterministically.
• Difficulty and operation filters work as configured.
• Scores and match completion remain synchronized.
• EXIT works from either board in every phase.
• Pure rules pass strict host compilation with -std=c++17 -Wall -Wextra -Werror.
• Encrypted PlatformIO firmware builds successfully.
• Both CYDs are flashed and physically verified for readability, touch accuracy, timing fairness, and bilateral EXIT.