THE WENBU LIBRARY

How three coins become an I Ching hexagram

A clear guide to 6, 7, 8 and 9, bottom-to-top line order, changing lines and the difference between a cast and an interpretation.

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THE SHORT ANSWER

In the three-coin method, one toss of three coins produces one line. Six tosses build the figure from bottom to top. Totals of 6 and 8 begin as yin; 7 and 9 begin as yang. Only 6 and 9 change. Keep all six numbers so another reader can reconstruct both hexagrams.

  • Each number records both a line’s shape and whether it changes. Copying only solid and broken lines loses part of the cast.
  • The first toss is the bottom line. A compound name such as Lake over Water names the upper trigram first; that is a different order from the casting record.
  • The four totals are not equally likely. Wenbu adds three independent fair binary outcomes, preserving the 1:3:3:1 distribution for 6, 7, 8 and 9.
ILLUSTRATED NOTE

Select a line to cycle through 6 → 7 → 8 → 9. This changes only the teaching diagram; it does not cast or save a reading.

Original
Resulting
6⚋
5⚊
4⚋
3⚋
2⚊
1⚊

47 · Constraint → 60 · Boundaries
Vermilion marks changing lines. Line 1 is at the bottom.

Default example · Two states of one cast: only lines 1 and 4 change

Read 6, 7, 8, 9, 7, 8 from bottom to top. The original is Lake over Water, Kun 困, number 47. Flipping the first and fourth lines gives Water over Lake, Jie 节, number 60. The other four lines stay unchanged.

Choose a convention before casting

Assign 2 to one side of a coin and 3 to the other. Toss three coins and add their values: the total is 6, 7, 8 or 9. Which side receives which value matters less than keeping the convention consistent.

Repeat six times. The first line belongs at the bottom of the hexagram; later lines are placed above it. Reversing this order changes the hexagram, so label a manual record clearly.

Four numbers, two line shapes

Seven is young yang, a solid line. Eight is young yin, a broken line. Nine is old yang: solid, changing to broken. Six is old yin: broken, changing to solid. Six and nine are changing lines.

Three fair coins have eight equally likely combinations. The probabilities of 6, 7, 8 and 9 are 1/8, 3/8, 3/8 and 1/8. The traditional yarrow procedure has a different changing-line distribution and should not be presented as the same method.

From a coin total to a line

TotalCoin combinationsOriginal lineResulting line / probability
6 · Old yin2 + 2 + 2; one arrangementBroken, changingBecomes solid; 1/8
7 · Young yangTwo 2s and one 3; three arrangementsSolid, stableStays solid; 3/8
8 · Young yinOne 2 and two 3s; three arrangementsBroken, stableStays broken; 3/8
9 · Old yang3 + 3 + 3; one arrangementSolid, changingBecomes broken; 1/8

On a small screen, scroll the table sideways.

The original and resulting hexagrams

Draw the original hexagram from the six line values. Flip only the changing lines to construct the resulting hexagram. If none change, the two are identical. This transformation is deterministic and can be checked independently of an AI interpretation.

Wenbu simulates coin outcomes with cryptographic randomness and also accepts physical coin results. The six values, changing positions and King Wen numbers remain visible for review.

Where to begin when several lines change

Traditions differ on how to read multiple changing lines. Wenbu shows every changing position rather than claiming a universal selection rule. The short themes are original reflection prompts, not quotations from a classical edition.

Begin with an open, concrete question. Record what the imagery brings to mind and revisit the note later. What you overlooked and what you actually did can be more useful than repeatedly casting until an answer feels comfortable.

Check the process with six numbers

Write 6, 7, 8, 9, 7, 8 in bottom-to-top order. Lines one and four change: the first changes from yin to yang, the fourth from yang to yin. The other four stay as they are.

Enter these as manual coin results in Wenbu and check the changing positions before reading the names. This is a worked example of the transformation, not a cast for a real-life question.

WORKED EXAMPLE

Check the whole transformation: 47 to 60

This is a teaching example, not a random reading for you. Draw six numbered spaces with line 1 at the bottom. Enter 6, 7, 8, 9, 7, 8 in that order.

  1. Draw broken lines at positions 1, 3 and 6, and solid lines at 2, 4 and 5. Leave the original numbers alongside them before reading any interpretation.

  2. Separate the figure into lower and upper groups. The bottom three form Kan, Water; the top three form Dui, Lake. The lookup is Lake over Water: Kun 困, number 47.

  3. Flip only the changing positions. The 6 at line 1 becomes solid; the 9 at line 4 becomes broken. Do not reverse the entire diagram or alter a stable line.

  4. Identify the new groups: Lake below, Water above. This is Jie 节, number 60. Save the six numbers, changing positions 1 and 4, and both hexagram names together.

  5. Ask an Agent to repeat those details before interpreting them. If it selects one changing line over another, request its reading convention. A claim to quote the classic needs a passage and line reference.

The checkable result is the structural change from 47 to 60. Reading it as “meet constraint with moderation” is a possible modern association, not a causal fact established by the numbers.

Key terms

Yao 爻
One line of a hexagram, numbered from the bottom upward.
Changing line
A line valued 6 or 9 in this coin method; it flips when constructing the resulting figure.
Resulting hexagram
The figure after every changing line flips, often called the relating hexagram or zhi gua 之卦.

Common questions

Should I cast again if no lines change?

No. Each line has a 3/4 chance of being stable, so a six-line cast has about a 17.8% chance of having no changes. Record that outcome. The two hexagrams are identical; a second cast is not needed to make the first one valid.

Are digital coins more accurate than physical coins?

Wenbu uses the same numerical distribution as three fair coins. Physical outcomes may also depend on the coins and how they are tossed. Matching a probability model does not establish predictive power. Manual entry is useful when you want to keep a physical casting process.

What should I give another Agent for a reproducible check?

Provide the six numbers, the bottom-to-top order, the three-coin method, the original number and the changing positions. An unlabeled screenshot cannot distinguish 6 from 8 or 7 from 9, so it may not contain enough information to reconstruct the resulting hexagram.

Sources and their scope

Wenbu · src/lib/iching.ts ↗

Supports the probabilities, bottom-to-top order, changing-line algorithm and random/manual modes; the example is checked against this implementation.

《周易》· 困 ↗

Primary text for hexagram 47 and its line texts, separate from the original reflection exercise.

《周易》· 节 ↗

Primary text for Jie, the resulting hexagram; it is not cited as documentation for the software’s random algorithm.

Chinese Text Project · Book of Changes ↗

Further reading; not validation of real-world predictions.

Book of Changes · Xi Ci I ↗

Further reading; not validation of real-world predictions.

Traditional interpretations are not established predictions. See the source notes for context.

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ADDITIONAL PRACTICE · 2026-11-13

Check a three-coin record when you forgot which face counted as three

Coin-cast check worksheet: complete answer keys and mismatch debugging

To catch line-order and changing-line mistakes, fill a six-row worksheet before looking up any name: position (1 at the bottom), raw value, original line, changing status and resulting line. Then check three things: every value is 6, 7, 8 or 9; the changing rows are exactly those holding 6 or 9; and the resulting figure flips only those rows. Once the structure passes, match the trigrams to the names. Both hypothetical data sets below come with complete answer keys so you can locate the faulty row.

  • Number the worksheet 1–6 from the bottom up and put the first toss in the lowest row; copying from the top of a page inverts the whole figure.
  • Changing status depends only on the value 6 or 9, not on the line shape; a broken line may change and a solid line may stay.
  • The resulting figure flips only the changing rows; the other rows must stay identical, and flipping the whole figure or missing a row changes the name.

From six values to two hexagram names

  1. Step 1: fix the order

    Write the six tosses into rows 1–6 from the bottom up, with row 1 as the earliest toss.

  2. Step 2: draw the original

    Write broken for 6 and 8, solid for 7 and 9, keeping the raw values beside them.

  3. Step 3: mark changes

    Mark only 6 and 9 as changing, label every other row stable, and count the changing rows.

  4. Step 4: flip only those rows

    Change the shape in changing rows, leave the rest untouched, then look up both names.

  5. Step 5: compare with the keys

    Check both hypothetical sets: 6, 7, 8, 9, 7, 8 is Kun 47 to Jie 60; 8, 7, 6, 7, 9, 8 is Kun 47 to Heng 32.

Fix the order, set the shapes, mark changing lines, flip only those rows, then compare both names with the answer key.

The six-row worksheet: structure before names

Make a six-row table with columns for position, raw value, original line, changing status and resulting line. Number positions 1 to 6, with row 1 as the bottom line. Fill one row per toss and look up names only after all six rows are complete, so an error stays attached to a specific row instead of hiding in the whole picture.

Keep the raw numbers rather than only solid and broken marks. A value records two things: yin or yang sets the current shape, and young or old decides whether it changes. If you copy only shapes, you can no longer tell which rows should flip or explain the cast to someone else.

Three mismatches and a fixed check order

The first mismatch is order: writing the first toss at the top, which turns the figure upside down; check that row 1 holds the earliest number you recorded. The second is changing status: marking a 7 or 8 as changing, or missing a 6 or 9; check that the number of changing rows equals how often 6 and 9 appear. The third is transformation: flipping stable rows or reversing the entire figure; check that only changing rows differ.

Use a fixed order: verify the value range, then the changing positions, then the resulting figure. Only then move to names and interpretation. If you ask an Agent to review, have it restate the six values, their order, the changing positions and both names before discussing meaning; if it claims to quote the classic, ask for the passage and line reference.

Two answer keys: same original, different result

First set, 6, 7, 8, 9, 7, 8: lines 1, 3 and 6 are broken and lines 2, 4 and 5 are solid, so the lower trigram is Kan and the upper is Dui. The original is Lake over Water, Kun 困, number 47. Changing lines are rows 1 and 4; after flipping, the lower trigram becomes Dui and the upper becomes Kan, giving Water over Lake, Jie 节, number 60.

Second set, 8, 7, 6, 7, 9, 8: lines 1, 3 and 6 are broken and lines 2, 4 and 5 are solid, so the lower trigram is again Kan and the upper again Dui. The original is also Kun 困, number 47. Changing lines are rows 3 and 5; line 3 turns from yin to yang and line 5 from yang to yin, so the lower trigram becomes Xun and the upper becomes Zhen, giving Thunder over Wind, Heng 恒, number 32. Same original, different result: the changing positions decide it.

Six-row worksheet template with two answer keys (Kun 47 to Jie 60; Kun 47 to Heng 32)
PositionRaw valueOriginal lineChanging status and resulting line
1 (bottom)6 or 8Broken6 changes to solid; 8 stays broken
27SolidStable; stays solid
38 or 6Broken8 stays broken; 6 changes to solid
49 or 7Solid9 changes to broken; 7 stays solid
57 or 9Solid7 stays solid; 9 changes to broken
6 (top)8BrokenStable; stays broken

Hypothetical practice: how each data set reaches its answer key

Both sets below are hypothetical teaching data, not a cast for any real question and not a randomly drawn result. Fill the worksheet first without looking up names, then compare with the answer key.

  1. First set, bottom to top: 6, 7, 8, 9, 7, 8. Row 1 is 6, broken and changing; row 2 is 7, solid and stable; row 3 is 8, broken and stable; row 4 is 9, solid and changing; row 5 is 7, solid and stable; row 6 is 8, broken and stable.
  2. First-set checks: all values fall between 6 and 9; changing rows are 1 and 4, exactly where 6 and 9 appear; only those rows change shape. Kan below and Dui above give Kun 困 47; after flipping, Dui below and Kan above give Jie 节 60.
  3. Second set, bottom to top: 8, 7, 6, 7, 9, 8. Row 1 is 8, broken and stable; row 2 is 7, solid and stable; row 3 is 6, broken and changing; row 4 is 7, solid and stable; row 5 is 9, solid and changing; row 6 is 8, broken and stable.
  4. Second-set checks: changing rows are 3 and 5, exactly where 6 and 9 appear; only those rows change. The original shapes match the first set, so it is also Kun 困 47; after flipping, Xun below and Zhen above give Heng 恒 32.
  5. Compare the sets: the original is the same and the result differs only because the changing positions differ. If row 4's 7 in the second set were wrongly marked as changing, the result would gain an extra flip and the name would be wrong; the worksheet exposes this immediately.

The observable result is that the first set changes at rows 1 and 4, taking Kun 47 to Jie 60, while the second changes at rows 3 and 5, taking Kun 47 to Heng 32. What the imagery might mean for real life belongs to interpretation; the worksheet checks structure, not fortune.

Questions you may have

The number of changing lines does not match the values. Where do I look first?

Return to the raw-value column and confirm each number really came from adding one toss of three coins, rather than a copying error or two tosses merged. Changing lines can only come from 6 and 9, so their count must equal how often those values appear. A mismatch points to the record, which should be corrected before any name is read.

Why do two data sets share an original but have different results?

Because the changing positions differ. The first set changes at rows 1 and 4, turning Kan below into Dui and Dui above into Kan, which gives Jie 60. The second changes at rows 3 and 5, turning Kan below into Xun and Dui above into Zhen, which gives Heng 32. The original depends only on the yin and yang of the six values; the result also depends on which rows are 6 or 9.

Terms in this guide

Answer key
The correct changing positions and two hexagram names for a hypothetical data set, used to compare a filled worksheet rather than to judge real-life fortune.
Mismatch debugging
Checking a worksheet in a fixed order for order, changing-status and transformation errors so each mistake can be traced to a specific row.
See the claim and source notes
  • In the three-coin method each line takes 6, 7, 8 or 9; six lines run bottom to top, and 6 and 9 are the changing lines that flip to form the resulting hexagram.

    6 与 9 是动爻
  • Traditions differ on how to use multiple changing lines; the tool displays all changing lines rather than naming one rule as the only standard, so structural checks come first.

    本工具展示全部动爻
  • The existing guide already gives the full 6, 7, 8, 9, 7, 8 transformation from Kun 47 to Jie 60, which serves as the basis for an answer key.

    Kun 困, number 47

Sources and review scope

Wenbu drafted and checked this article in Codex. The source list records the scope of the review.

  1. Current complete zh canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-05 · Fetched text
  2. Current complete en canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-05 · Fetched text
  3. Wenbu · three-coin method ↗Existing editorial and worked calculation · 2026-11-05 · Fetched text
  4. Wenbu · calculation conventions ↗First-party implementation; not evidence of predictive accuracy · 2026-11-05 · Fetched text

Choose manual coin entry in Wenbu

Enter the worksheet's six values from bottom to top, compare the changing positions and both hexagram names the tool shows with your table, and only then read the names.

Choose manual coin entry in Wenbu ↗

Explore this guide with Wenbu ↗

The same hexagram can hide a reversed six-line record

A matching primary hexagram is not enough to verify the order of a cast. Reverse the six numbers in the exercise below and the primary figure still reads Li. Its moving lines and relating hexagram change. To catch the error, compare the original numbers from the bottom line upward, then check where the moving lines fall.

  • Identical primary figures can conceal different moving lines.
  • Keep the six values with their line numbers, even if you also save a picture.
  • Use the numbered cast to decide which entry is correct.

Check three layers in order

  1. Raw values

    Read the numbered throws from bottom to top.

  2. Moving lines

    Circle the 6 and the 9 and mark their positions.

  3. Relating figure

    Flip only the marked lines.

The primary figure matches in this exercise; the moving-line check is where the two records diverge.

Why checking the figure misses this error

The bottom-to-top record is 9, 8, 7, 7, 6, 7. Both 7 and 9 draw a solid line. Both 6 and 8 draw a broken line. The resulting solid, broken, solid, solid, broken, solid pattern is symmetrical. Read it backward and the primary figure still looks the same. A check against the hexagram name or the picture alone will pass the reversed entry.

Now circle the 6 and the 9. In the original record they are on lines 5 and 1. In the reversed record they are on lines 2 and 6. Both records have two moving lines, but different lines get flipped. Entering the two fixed sequences in Wenbu gave the same primary hexagram, 30 (Li), followed by 33 in the original and 34 in the reversal.

How to check the entry against your notes

Label each value as you go, from line 1 at the bottom to line 6 at the top. If you sketched the diagram with the top line first on the page, that sketch is still a top-down drawing of a bottom-up record. Read the line labels before transcribing. The first number that disagrees with your numbered notes tells you where to investigate.

A saved picture without moving markers or throw numbers cannot settle what happened. Record the figure you can see and mark the original sequence as unverified. When you find the notes, preserve the old entry and make a corrected copy that says what changed. The interpretation of either relating figure tells you nothing about which transcription was correct.

One cast and its reversed transcription
Bottom-to-top entryPrimary and moving linesRelating
9, 8, 7, 7, 6, 730 Li; 1 and 533 Dun
7, 6, 7, 7, 8, 930 Li; 2 and 634 Dazhuang
Unmarked diagram onlyShows the shape of 30 Li; the values and moving positions are unverifiedUnresolved

Find the transcription error without reading either figure

Cover the last two columns. Treat the first row as the numbered original and compare the two rows with six values.

  1. Write the position next to each 6 or 9 in both rows.
  2. Draw the primary lines using 7/9 for solid and 6/8 for broken. Compare the drawings.
  3. Flip the marked lines and compare the results with the last column.

The throw numbers identify the correct record. Both calculated relating figures are consistent with their respective inputs.

Questions you may have

Is a count of moving lines enough?

No. The count is two in both versions. Compare the numbered moving positions at minimum, and return to the full set of raw values if the notes are available.

Can I reconstruct the six numbers from an unmarked picture?

No. A solid line could be 7 or 9, and a broken line could be 6 or 8. Leave those values unknown if you have no original record to check.

Terms in this guide

Primary hexagram
The figure drawn from the initial solid and broken lines.
Moving-line position
A numbered line, counted from the bottom, whose original value was 6 or 9.
See the claim and source notes

Sources and review scope

Wenbu drafted and checked this article in Codex. The source list records the scope of the review.

  1. Current complete zh canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-11 · Fetched text
  2. Current complete en canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-11 · Fetched text
  3. Wenbu · three-coin method ↗Existing editorial and worked calculation · 2026-11-11 · Read excerpt
  4. Wenbu · calculation conventions ↗First-party implementation; not evidence of predictive accuracy · 2026-11-11 · Fetched text

Recalculate both six-number records

Use manual entry for each row of the table. Compare the primary figure, moving positions and relating figure with the key.

Recalculate both six-number records ↗

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Keep each toss at its original line position and score the faces in two columns, one with heads worth 3 and one with tails worth 3. The paired totals always add to 15. Six and nine switch, as do seven and eight. The moving positions agree while the line polarities reverse. Keep both candidate results if the notebook contains no evidence of the original scoring rule.

  • Keep the actual face records and original positions.
  • Check that paired totals add to 15 and the moving lines agree.
  • Keep two candidate readings until the scoring rule can be recovered.

From recorded faces to two candidate casts

  1. Keep the order

    Write the first toss at the bottom line, then work upward.

  2. Add the faces twice

    Apply both assignments and check that each pair of totals adds to 15.

  3. Check moving lines

    Compare their positions in both outputs and retain the uncertainty about scoring.

Hold the tosses and their line positions fixed. Use one score assignment throughout each column.

Use two score columns for each toss

Draw two columns. Use H for heads and T for tails. In one, H is 3 and T is 2. In the other, H is 2 and T is 3. For HHT, the first column adds 3, 3 and 2 to make 8. The other adds 2, 2 and 3 to make 7. Each coin contributes 5 across the two columns, so every row adds to 15 without requiring you to know which rule the original writer preferred.

An all-matching toss gives 6 in one column and 9 in the other. Both are moving lines. A toss with mixed faces gives 7 and 8, so it stays fixed in both candidates. If the moving positions differ, inspect the copied tosses and line order before considering either result. The arithmetic check confirms the comparison you made today.

Keep what agrees and mark what remains open

In the table below, the first column gives The Traveler changing to Repair. The other gives Boundaries changing to Adaptation. Lines two and four move in both. Compare original with original and relating with relating. In each pair, one figure has a solid line wherever its counterpart has a broken line.

Look for a scoring key on the same page or a verified total attached to one of these tosses. One confirmed total from the same session can separate the candidates because the paired totals never match. If the evidence is absent, write “scoring rule unknown, lines two and four moving” and retain both results.

Six tosses and two scoring assignments
Line, bottom upRecorded facesH counts as 3T counts as 3
1HHT87
2TTT69
3HTT78
4HHH96
5HTH87
6THT78

Check both candidates by entering the totals

This fictional notebook contains the six H and T rows above. The line order is known. The scoring key is missing.

  1. With H worth 3 and T worth 2, enter 8, 6, 7, 9, 8, 7 from the bottom up. The Traveler (56) changes to Repair (18).
  2. With H worth 2 and T worth 3, enter 7, 9, 8, 6, 7, 8 in the same order. Boundaries (60) changes to Adaptation (17).
  3. Both receipts mark lines two and four. If an original note later verifies that the second line was 6 on this cast, it identifies the first assignment.

Keep both candidate casts, and keep lines two and four as the moving positions confirmed by the face record.

Questions you may have

Can the moving positions tell me which face scored 3?

They cannot. Both assignments mark an all-matching toss as a moving line and reverse its direction of change. To choose an assignment, find the original score key or a verified total attached to one of the same tosses.

Does a paired sum of 15 prove the original scoring rule?

It checks that the current comparison swapped the scores and added them consistently. A rule or confirmed total from the original record is needed to choose a column.

What if I lost the order of the tosses too?

Mark the line positions as unknown. This exercise compares scoring assignments once each toss is already matched to its line from bottom to top.

Terms in this guide

Score assignment
The choice of which face of a coin counts as 2 and which counts as 3.
Face record
A notation such as HHT that preserves the faces of the three coins in one toss.
See the claim and source notes

Sources and review scope

Wenbu drafted and checked this article in Codex. The source list records the scope of the review.

  1. Current complete zh canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-13 · Fetched text
  2. Current complete en canonical article ↗Current public original and earlier additions; add substantial coverage without repeating or replacing them. · 2026-11-13 · Fetched text
  3. Wenbu · calculation conventions ↗First-party implementation; not evidence of predictive accuracy · 2026-11-13 · Fetched text
  4. Wenbu · versioned public capabilities ↗First-party current tool, convention and privacy contract; not external endorsement or predictive validation · 2026-11-13 · Fetched text

Check both columns in the I Ching tool

Choose Enter coin results. Keep the original line order and compare the two sets of figures and moving lines.

Check both columns in the I Ching tool ↗

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