Find Full-Time Timestamps
十全时 · Use every digit from 0 through 9 exactly once
Build a valid 2014 date and time, encode it as ten digits, then search systematically for every moment whose digits are a perfect permutation of 0–9.
Your calendar and clock reference
Use two digits for each field, including a leading zero when needed. The first pair is the month; the fourth pair is the minute. The fixed year 2014 is not written in the code.
- 2014 is not a leap year: February has 28 days.
- April, June, September, and November have 30 days. The other months have 31.
- Hours run from 00 to 23. Minutes and seconds run from 00 to 59.
Try a prediction before using a search tool. Local hints below explain the method without giving the final discoveries. Complete all eight stages for the optional badge.
Progress saves in this browser.
Encode one moment as ten digits
Use two digits each for month, day, hour, minute, and second. The year is understood to be 2014 and is not written in the code.
Worked example
The worked example encodes November 28 at 14:58:32 as:
Why two digits?
Two-digit fields keep every code the same length. March is written 03, 7 seconds is written 07, and the hour field at midnight is 00.
Decode the format
Local hint: Keep the five pairs in order.
Read month, day, hour, minute, second. A leading zero occupies a real place; omitting it would change the code length.
Define a Full-Time timestamp
A timestamp is “Full-Time” when its ten written digits are exactly 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9—each used once.
Digit inventory for the worked example
Three separate requirements
- The date must exist in the 2014 calendar.
- The time must exist on a 24-hour clock.
- The ten digits must form one complete set from 0 through 9.
A permutation alone is not enough. A code can use all digits once and still describe an impossible date or time.
Rule check
Local hint: Count each digit separately.
A repeated digit means some other digit must be missing from a ten-digit code. A valid date and time can still fail this digit rule.
Validate any candidate
Enter all five fields and predict the first test that will fail, or predict that all tests will pass. A correct diagnosis of a fully entered candidate completes this stage; you do not need to discover a Full-Time moment yet.
Local hint: Check the calendar before the digit inventory.
First fill every field with a whole number in the stated range. The tool adds a leading zero for one-digit entries. A day such as February 30 fails the calendar test. For a valid date and time, count the ten written digits. A correct prediction completes this diagnosis stage, even when the candidate is not Full-Time.
Design a complete search
A good search finds every solution once, rejects impossible branches early, and does not examine all 31,536,000 seconds one by one.
Efficient search plan
Why this is complete
Every valid timestamp has one month, one day, one hour, one minute, and one second. The loops visit every possible first four fields. If those eight digits are distinct, the final two digits are forced to be the two digits not yet used.
No duplicates: one timestamp has only one decomposition into MM · DD · hh · mm · ss.
Search-plan check
Local hint: Reject a branch as soon as a digit repeats.
Once eight different digits fill month, day, hour, and minute, only two digits are unused. Test both possible orders as seconds, keeping only 00–59. This is exhaustive: every possible last pair is included.
Search 2014 month by month
Select each month. The page searches that month and counts its qualifying date-and-time codes. Count each whole-second code once; this is a calendar puzzle, so time zones and clock changes are not part of the rules. Search all twelve months before drawing a conclusion.
| Month | Status | Discovered count |
|---|
Selected month
Choose a month to run its search.
Browse matches in time order
After searching a month, choose a rank (position in its time-ordered list) from 1 through that month’s discovered count. A month with zero matches has no valid rank. Rank 1 is the earliest match in that month; the largest rank is its latest match.
Local hint: Make a prediction before clicking a month.
Look at the two month digits and eliminate any branch that already repeats a digit. After searching, note whether the result supports your prediction. The indexed browser sorts each month chronologically; rank 1 is its first match, and the largest allowed rank is its last.
Hunt the earliest and latest moments
Enter each answer as one ten-digit MMDDhhmmss code, with no spaces or punctuation. MM is month; DD is day; hh is hour; mm is minute; ss is second. The checker says whether your candidate is valid and whether another Full-Time moment occurs earlier or later.
Earliest candidate
Latest candidate
Local hint: Compare fixed-length codes from left to right.
All fields use two digits. Compare the month first, then day, hour, minute, and second. Search earlier calendar branches for the earliest moment and later branches for the latest. A valid candidate is not necessarily a boundary.
Count every moment and identify the active months
Use your month ledger. Enter the grand total and select every month that contains at least one Full-Time moment.
Grand total
The checker reports only whether your total is too low, too high, or correct.
Months with at least one match
Local hint: Use the complete month ledger.
Visit every month, including ones with zero matches. Add the twelve counts exactly once. Select a month only if its searched count is positive. Recheck the ledger rather than guessing from feedback.
Explain why your search is complete
Finish with the logic that turns a computer search into a mathematical enumeration rather than a lucky hunt.
Completeness audit
Full-Time Timestamp Enumerator
This certifies that
decoded, searched, counted, and verified the 2014 Full-Time timestamps.
This optional badge does not change Chapter 16 mastery.
Local hint: Explain coverage and uniqueness separately.
Coverage means every valid date, hour, and minute was visited and both remaining-second orders were tested. Uniqueness means each code has only one split into the five fixed-width fields. You need both claims to prove an exact count.
Teaching notes
The original defines a ten-digit month-day-hour-minute-second code for 2014 and gives a result summary.
This student page intentionally omits that summary. Its verifier generates all valid moments directly from the stated rules at runtime. The month search and indexed browser are discovery tools that the student controls; no static answer key is embedded in the lesson text.
The enumeration uses the 2014 calendar, 24-hour time, and exact digit masks. After month, day, hour, and minute use eight different digits, the two remaining digits are tested in both orders as the second field.