feat(learn): teach the last-two-digits ÷4 leap shortcut (#7) - #27
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Stage 2 only gestured at the fast path ("for 2001–2099, just ask ÷4?"). State the
actual trick: for any non-century year only the last two digits matter for the ÷4
test — the hundreds always end in 00 and 100 is a multiple of 4, so they never
change the remainder. Verified exact for every non-century year across the full
proleptic range (9999 BC–9999 AD), 0 counterexamples vs isLeapYear.
- curriculum.ts: replace the weak "2001–2099: just ÷4" line with a shortcut
paragraph (two-digit examples 1968→68, 2008→08) + mnemonic; xx00 → ÷400 stays
the only carve-out. Full Gregorian rule, mnemonic, worked list, and the Jan/Feb
shift paragraph all kept.
- CheatSheet.tsx: generalize "(2001–2099: just ÷4.)" → "(Non-century year: last
two digits ÷4.)" so the cheat-sheet matches the lesson.
- curriculum.test.ts: lock the shortcut copy against regression.
Gates: typecheck, lint, tests, build — all green.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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The Stage-2 guard checked `toContain('00')`, which is satisfied by
incidental tokens (1900/2000/2100/2008) and passed against the old copy
too — so it guarded nothing about the new last-two-digits shortcut.
Assert the carve-out wording itself ('unless they are 00').
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Closes #7. Roadmap item 3/7.
Stage 2 "Leap years" only gestured at the fast path with one weak line ("For everyday dates in 2001–2099, just ask: divisible by 4?"). This states the actual mental trick.
The shortcut (research-verified)
For any year not ending in 00, only the last two digits matter for the ÷4 test — the hundreds always end in
00and100 = 4×25is a multiple of 4, so they never change the remainder (Y ≡ last-two-digits (mod 4)). An executable sweep in the research pass confirmed this is exact for every non-century year across the full proleptic range (9999 BC–9999 AD) — 0 counterexamples vs the engine'sisLeapYear.Changes
curriculum.ts— replace the weak2001–2099line with a shortcut paragraph (two-digit examples1968 → 68,2008 → 08) + mnemonic "Last two digits ÷4 — unless they are 00, then ÷400." The framing keeps last-two-digits-÷4 as the everyday rule andxx00 → ÷400as the only carve-out (not the reverse). The full Gregorian rule, the÷4/÷100/÷400mnemonic, the2024/1900/2000/2100worked list, and the Jan/Feb-shift paragraph are all kept.CheatSheet.tsx— generalize(2001–2099: just ÷4.)→(Non-century year: last two digits ÷4.)so the cheat-sheet agrees with the lesson. (This file was missing from the issue's affected-files list — flagged by the research.)curriculum.test.ts— assert Stage 2's copy contains the shortcut + the00carve-out, guarding against regression.Verification
typecheck ✓ · lint
--max-warnings 0✓ · tests ✓ · build ✓. No engine change (doomsday.test.tsalready coversisLeapYearground truth).🤖 Generated with Claude Code