Daily Five-Question DPP Leaderboard

ROLE: Act as a daily-practice designer, Google Forms developer and privacy-aware Sheets leaderboard builder.

CONTEXT: A teacher wants a five-question phone DPP on [DAILY SKILL] with immediate collection and a transparent class leaderboard.

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS OR BATCH]
- [DAILY SKILL]
- [DATE OR DAY NUMBER]
- [DIFFICULTY PATH]
- [MARKS PER QUESTION]
- [STUDENT LABEL FIELD]
- [TIEBREAK RULE]

DO THIS:
1. Write exactly five original questions progressing from warm-up to exam-level application.
2. Give a compact review key with solutions and check-this-yourself links for all calculations.
3. Generate one complete executable FormApp quiz script with a student-label field, correct choices, points, linked response sheet and logged URLs.
4. Output a Google Sheets leaderboard formula that filters blanks, totals scores, sorts descending and applies the stated tiebreak rule.
5. Show a small fictional formula test table and the resulting rank order without exposing real student data.
6. Add a privacy note offering initials or roll codes instead of public names.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Make a five-question DPP on factors and multiples ending with lcm(12,18).
Expected result or check target: The verified LCM is 36, and a correct response receives the item’s points before the total enters the leaderboard.
check this yourself
CHECK → https://www.wolframalpha.com/input?i=lcm%2812%2C18%29
(paste-fallback: lcm(12,18))
Encoding note: The parentheses are %28 and %29, and the comma is %2C.

OUTPUT FORMAT:
1. FIVE-QUESTION DPP REVIEW
2. VERIFIED KEY
3. COMPLETE GOOGLE APPS SCRIPT
4. RUN IT — script.google.com → New project → paste → Run → View → Logs
5. LEADERBOARD SHEET FORMULA
6. FORMULA TEST TABLE
7. PRIVACY-SAFE SHARING NOTE

QUALITY AND TOOL GUARDRAILS:
- Output one COMPLETE executable Google Apps Script code block using FormApp with all five questions and linked-sheet setup included.
- After the code, print exactly: script.google.com → New project → paste → Run → View → Logs.
- The leaderboard formula must use actual columns created by the script and must not expose email addresses or other private data.
- Never claim a URL creates the form; verification links are for checking maths only.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.