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# System prepended metadata

title: More Groupokus

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# More Groupokus 

([home](https://github.com/alexhkurz/introduction-to-numbers/blob/master/README.md) ... [previous](https://hackmd.io/@alexhkurz/B1w9oSPiL) ... [next](https://hackmd.io/@alexhkurz/S17OoT2oI))

Recall the rules of [Groupoku](https://hackmd.io/@alexhkurz/B1w9oSPiL):

- Every row and column needs to contain every number exactly once (unique solution to equations $ax=b$).
- The top-left down-right diagonal gives a mirror symmetry (commutativity).
- At the end we need to check for associativity using the program [groupoku](https://github.com/alexhkurz/introduction-to-numbers/blob/master/src/groupoku.py).

**Groupoku:** Show that there is one and only one solution to

|0| 1| 2| 3|
|:---:|:---:|:---:|:---:|:---:|
| 1 |3||
| 2||||
| 3||||


**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|
|:---:|:---:|:---:|:---:|:---:|
| 1 |0||
| 2||0||
| 3||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|
|:---:|:---:|:---:|:---:|:---:|
| 1 |0||
| 2||1||
| 3||||


**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|2||
| 2||3||
| 3||||
| 4||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|2||
| 2||4||
| 3||||
| 4||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|3||
| 2||1||
| 3||||
| 4||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|3||
| 2||4||
| 3||||
| 4||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|4||
| 2||1||
| 3||||
| 4||||

**Groupoku:** Show that there is exactly one solution to

|0| 1| 2| 3|4
|:---:|:---:|:---:|:---:|:---:|
| 1|4||
| 2||3||
| 3||||
| 4||||

