Permutrix

the game based on the VMPC one-way function


playing instructions step by step:

The purpose of the game is to fill the table with numbers. This is an example Permutrix:

And this is how it looks done:

- numbers in columns B and C are the same.
- numbers in columns D and E differ by 1.
- the pair of numbers repeats in all three blocks.

Permutrix rules:

Fill each column of the table with different numbers from 1 to 6 and this way form 6 pairs of numbers. A pair is two numbers lying side by side in one block. Put each pair in the table 3 times, each time in a different block. The order of numbers is important, e.g. and are different pairs. Additionally:

1. Numbers lying side by side in columns B and C are the same. E.g.

2. Numbers lying side by side in columns D and E differ by 1. E.g.
The number greater by 1 in column E. An exception in columns D and E:

Step 1.
Newly entered numbers in a given step with be red.

Numbers lying side by side in columns B and C are the same. In column C there is a 3 so in column B side by side we can enter also 3. Numbers lying side by side in columns D and E differ by 1. In column D there is a 1 so in column E side by side we can enter 2.



Step 2.

We can see numbers 1 and 3 lying side by side in one block (the AB block). So they are a pair. We can remember that each pair must appear in the table 3 times - once in each block. We can see a 3 in block EF and that it fits to our 1|3 pair. Therefore we can enter 1 next to that 3. This way we already have two blocks where the 1|3 pair appears.

Step 3.

Numbers lying side by side in columns D and E differ by 1. There is a 1 in column E. 1-1=0 and while we can only use numbers from 1 to 6 then instead of 0 we rewind back to 6 in column D. This is the exceptional situation where numbers 6|1 lie side by side in columns D and E.

Step 4.

We can see numbers 2 and 1 lying side by side in one block (the EF block). So they are a pair. Each pair must appear once in each block. We can fit the 2|1 pair in both the AB and CD blocks. This way the 2|1 pair already appears in all three blocks!

Step 5.

Numbers lying side by side in columns B and C are the same. In column B there is a 1 so in column B side by side we can enter also 1. And similarly number 2 from column C can be copied to column B side by side.

Step 6.

We can see that a 1 appeared in column B so this is the place where we can enter the 1|3 pair which already appears in blocks AB and EF.

Step 7.

We can see the 5|2 pair in block AB. Because there is a 2 in column F, we can fit this pair there - in the EF block.

Step 8.

Numbers lying side by side in columns D and E differ by 1. In column D there is a 3, so side by side in E there will be 4. In E we can see a 5 so in D side by side we will have a 4.

Step 9.

We can see the 4|6 pair in block EF. We can fit this pair in both the AB and CD blocks.

Step 10.

Numbers lying side by side in columns B and C are the same. We can copy the 6 from column B to C and the 4 from column C to B.

Step 11.

We can see a new pair 6|4 which already appears in two blocks. We can also fit it to the third EF block.

Step 12.

In column E there is a 6 so side by side in D there will be a number smaller by one, a 5.

Step 13.

We can see a new pair 3|5 in block CD. It fits to two other blocks.

Step 14.

We copy number 5 from column B to C and to column D we enter number 2 which is smaller by one than number 3 side by side in column E.

And that's it!

Have fun!

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