# How to cast a Meihua Yishu hexagram from numbers

![A plum blossom twig with one open flower beside three plain bamboo counting rods](https://multifate.com/images/guides/meihua/meihua-three-number-casting/cover-v1-1536x864.webp)

> How to cast a Meihua Yishu hexagram from three numbers: which number sets each trigram, how the moving line is chosen, and how to check the result.

Canonical page: https://multifate.com/guides/meihua/meihua-three-number-casting
Language: English. Content reviewed: 2026-09-23.
Also available in: [中文](https://multifate.com/zh/guides/meihua/meihua-three-number-casting/index.md), [日本語](https://multifate.com/ja/guides/meihua/meihua-three-number-casting/index.md), [한국어](https://multifate.com/ko/guides/meihua/meihua-three-number-casting/index.md)

To cast a Meihua Yishu hexagram from numbers, give three whole numbers from 1 to 99: the first sets the upper trigram, the second the lower trigram, and the third the moving line. Meihua Yishu, often called plum blossom numerology, has other casting methods too. This guide follows the one the free Multifate tool uses.

**Key points**

- Three whole numbers from 1 to 99, in order, set the upper trigram, the lower trigram and the moving line.
- Trigrams use the remainder after dividing by 8 (0 counts as 8); the moving line uses the remainder after dividing by 6 (0 counts as 6).
- Lines count from the bottom. Flipping the moving line gives the changed hexagram; lines 2 to 5 give the mutual hexagram.
- The same numbers under the same rules always give the same hexagram, however you word your question.

## Numbers or time: which way should you cast?

The free tool casts in two ways: from three numbers, or from a moment in time that you confirm before the result is fixed. The two follow different input rules, so they are separate calculations, not two views of one hexagram. This guide follows the number method.

- By three numbers: three whole numbers from 1 to 99, kept in the order you entered them, because order matters.
- By a moment in time: a cast from the exact minute you confirm. Its rules differ, so do not check it against a number cast.

> **Tip** Your question gives the reading its context, but it never enters the arithmetic. Reword it, enter the same three numbers, and you get the same hexagram.

## How do three numbers cast a Meihua Yishu hexagram?

Each number has one job. The first and second are divided by 8, and their remainders pick the upper and lower trigrams; a remainder of 0 counts as 8. The third is divided by 6, and its remainder picks the moving line, where 0 means line 6.

![How to cast a Meihua Yishu hexagram: 11, 13 and 12 become the upper trigram, the lower trigram and the moving line](https://multifate.com/images/guides/meihua/figures/meihua-number-casting-en-v1-1200x608.webp)

Follow each number to its remainder, then to a trigram or a line\. 11 and 13 leave 3 and 5, giving Li over Xun; 12 leaves 0, which counts as 6, so the top line moves\. It is the same cast as the worked example below\.

*The number rule the free tool follows*

| Input | Sets | Rule |
| --- | --- | --- |
| First number | Upper trigram | Remainder after dividing by 8; 0 becomes 8 |
| Second number | Lower trigram | Remainder after dividing by 8; 0 becomes 8 |
| Third number | Moving line | Remainder after dividing by 6; 0 becomes 6 |

Some tutorials and calculators add the numbers together before choosing the moving line. That is a different rule, not an arithmetic slip, so compare methods before you suspect a mistake. To try the rule on your own numbers, use the [free Meihua Yishu calculator](https://multifate.com/tools/meihua).

## Which number is which trigram?

Each remainder from 1 to 8 names one of the eight trigrams, in the traditional Earlier Heaven (Xiantian) order below. Keep an eye on the element column: it matters later, when the reading compares the two trigrams.

*Remainders 1 to 8 and the trigram each one names*

| Number | Trigram | Image | Element |
| --- | --- | --- | --- |
| 1 | Qian 乾 | Heaven | Metal |
| 2 | Dui 兑 | Lake | Metal |
| 3 | Li 离 | Fire | Fire |
| 4 | Zhen 震 | Thunder | Wood |
| 5 | Xun 巽 | Wind | Wood |
| 6 | Kan 坎 | Water | Water |
| 7 | Gen 艮 | Mountain | Earth |
| 8 | Kun 坤 | Earth | Earth |

## A worked example, one step at a time

Take the numbers 3, 5 and 6, in that order.

1. **Find the upper trigram**: 3 divided by 8 leaves 3: Li, the trigram of fire, goes on top.
2. **Find the lower trigram**: 5 divided by 8 leaves 5: Xun, the trigram of wind, goes underneath.
3. **Find the moving line**: 6 divided by 6 leaves 0, which counts as 6, so line 6, the top line, moves.
4. **Name the primary hexagram**: Li over Xun is the primary hexagram Ding 火风鼎, the Cauldron.
5. **Name the changed hexagram**: Flipping line 6 turns the upper Li into Zhen 震, thunder, so the changed hexagram is Heng 雷风恒, Duration.

> **Cast record**
>
> Numbers: 3 · 5 · 6
> Upper trigram: Li
> Lower trigram: Xun
> Moving line: 6
> Primary hexagram: Ding
> Changed hexagram: Heng

Change the third number to 1 and the bottom line moves instead: the lower Xun becomes Qian 乾, and the changed hexagram is Da You 火天大有, Great Possession. The example shows order and line numbering only. It is not a reading of anyone's circumstances.

> **Tip** The figure's 11, 13 and 12 give exactly this cast, because only the remainders count.

## How to read the primary, mutual and changed hexagrams

The six lines are counted from the bottom. Lines 1 to 3 form the lower trigram and lines 4 to 6 the upper one, so a highlighted line 6 is the top line. The moving line flips between broken and unbroken; it is not a seventh line.

- **Primary hexagram**: The hexagram your numbers produce: the upper trigram stacked on the lower one.
- **Moving line**: The line the third number picks. It is a position in the primary hexagram, not another hexagram.
- **Changed hexagram** (Resulting hexagram): The primary hexagram with only the moving line flipped. The other five lines stay as they are.
- **Mutual hexagram** (Nuclear hexagram): Lines 2 to 4 of the primary form its lower trigram and lines 3 to 5 its upper. No line is flipped.
- **Ti and yong** (Body and use, Self and situation): Roles for the two trigrams: the one holding the moving line is yong, the other is ti. The display names how their elements relate.

![Cast a Meihua Yishu hexagram from 3, 5 and 6: primary Ding with ti and yong marked, mutual Guai and changed Heng](https://multifate.com/images/guides/meihua/figures/meihua-hexagram-trio-en-v1-1200x608.webp)

Lines count from the bottom\. In the primary hexagram Ding, line 6 moves, so the upper trigram Li is yong and the lower Xun is ti\. The mutual hexagram Guai is built from lines 2 to 4 and 3 to 5 of the primary; the numbers beside it show which primary line each of its lines copies\. The changed hexagram Heng flips line 6 and nothing else\.

In the example, the primary hexagram is Ding, and its mutual hexagram is Guai 泽天夬, Breakthrough. Ti and yong are decided on the primary hexagram, not the mutual one: the moving line sits in its upper trigram, so Li, Fire, is yong and Xun, Wood, is ti.

Wood feeds Fire, so ti generates yong. The tool labels that relation mildly unfavourable, traditionally a drain on the self, which is a classification and not a forecast. For the generating and controlling cycles behind this, see [BaZi five elements](https://multifate.com/guides/bazi/five-elements).

*The display's traditional labels, not a forecast*

| Relation | Label |
| --- | --- |
| Yong generates ti | Very favourable |
| Ti and yong share an element | Favourable |
| Ti controls yong | Favourable |
| Ti generates yong | Mildly unfavourable |
| Yong controls ti | Unfavourable |

> **Where the reading stops** Ti and yong, and labels such as favourable or unfavourable, are traditional associations. They do not measure anyone's body, health or odds of success.

## Why does another site give a different hexagram?

When two casts from the same numbers disagree, check these points in order before blaming the arithmetic.

1. **Order, range and method**: Same three numbers, same order, each from 1 to 99, cast by numbers rather than by time?
2. **Trigram numbering**: Are the trigrams numbered from 1 for Qian to 8 for Kun, as in the table above?
3. **Moving line rule**: Does the moving line come from the third number alone, or from a sum of the numbers?
4. **Line counting**: Is line 1 the bottom line? A source that counts from the top marks a different line.

The same valid numbers under the same rules always give the same hexagram. The wording of an AI interpretation can vary between requests, and a fixed calculation does not make every interpretation sound or turn it into a prediction.

## Bring one question to the cast

For example, if you are preparing for a difficult conversation, ask which part of it the primary and changed hexagrams help you think through. Keep what the cast contains apart from the facts you already know about that conversation. Good follow-up questions:

- What does the change at this line add to the primary hexagram?
- Which part of my description does that change relate to?
- Which claim in the answer relates to neither the cast nor my question?

Cast your own numbers with the [free Meihua Yishu calculator](https://multifate.com/tools/meihua), or read the [Meihua Yishu guide](https://multifate.com/guides/meihua) for an overview of the method. If you would rather work through a question with cards, see [how to read a three-card tarot spread](https://multifate.com/guides/tarot/how-to-read-three-card-tarot).

## Meihua Yishu casting: common questions

### What numbers can I use to cast a Meihua Yishu hexagram?

Three whole numbers from 1 to 99. Order matters: the first sets the upper trigram, the second the lower trigram and the third the moving line, so swapping the first two can change the hexagram.

### What if a number divides evenly by 8 or 6?

A remainder of 0 counts as 8 for a trigram, which is Kun, and as 6 for the moving line, which is the top line. So 16 as the first number puts Kun on top, and 12 as the third number moves line 6.

### Is the moving line the sum of all three numbers?

Not in this tool. The third number alone sets it, by its remainder after dividing by 6. Some tutorials use a sum, which is a different rule and can mark a different line.

### Why does another calculator give a different hexagram?

Usually the rules differ, not the arithmetic. Check the order of the numbers, the trigram numbering, where the moving line comes from and whether lines are counted from the bottom.

### Does changing my question change the hexagram?

No. The question sets the context of the reading, not the arithmetic. The same three numbers give the same primary, mutual and changed hexagrams however you word it. You can also cast with “Chart only” and ask a question afterwards.

## Sources and scope

- [Multifate Meihua tool](https://multifate.com/tools/meihua): The number inputs and the hexagram construction this guide explains. The arithmetic follows the tool's current implementation.

## Continue with Meihua

- [Try the Meihua tool](https://multifate.com/tools/meihua)
- [All Meihua articles](https://multifate.com/guides/meihua)
- [Fortune telling guides: BaZi, tarot and more](https://multifate.com/guides/index.md)

These guides describe traditional symbolic frameworks and the current Multifate tools, not verified predictions. The chart tools are free; optional AI questions have separate limits. Check the pricing page for current terms. Interpretations do not replace medical, legal, financial or safety advice.