# (Re-)Introducing KPK Puzzle!

Rules of KPK:

1. Put the letter K or P on every empty cell.
2. Clues outside the grid on the first row/column show how many letters ordered as "KPK" can be seen on the corresponding row or column.
3. Clues outside the grid on the second row/column show how many letters ordered as "PKP" can be seen on the corresponding row or column.

The genre of KPK is "not new" and has been introduced here as

• This puzzle is actually taken from the Instruction Booklet of a near-upcoming competition that I host: KPK 2021. The booklet contains the final solution -- without an explanation of course -- so proceed with caution! Sep 2, 2021 at 13:35
• I'm not shy, so I promoted it in chat for you. Hope you have a great contest, and I'm looking forward to solving :-) Sep 4, 2021 at 12:56
• Quality puzzle and a quality contest athin :) Had a crack at it just now and only made it through about 12 of the 30 puzzles in the time but at least now I have some leftovers to mull over during my lunch breaks this week! Thanks for pulling all of this together - all very impressive!
– Stiv
Sep 5, 2021 at 22:56
• @Stiv Thanks a lot Stiv for participating and with a happy feedback! We are glad our efforts have paid off. Though the difficulty level is way higher than we were first planning to, it's heartening to know people were satisfied and having fun! ^^ Sep 6, 2021 at 4:51

Solution

How I solved it
Step 1

First we focus on the rows and columns with digit '4'.
These can only be filled in with letters alternating

Step 2

Now look at the rows and columns with digit '0'.
We can fill in some more letters close to the Ks and Ps here.

Step 3

Now the fourth row is conspicuous. The only way we could have a 'PKP' here without a 'KPK' is if it were bookended by Ps and this can only happen in one place.

Step 4

Now look at the eighth column and notice that if we are to fit in three 'PKP's then the fifth element cannot be K, and so must be a P. Furthermore, either the second or sixth element must be a K (to allow three PKPs), but not both (since there is only one KPK). If the sixth element is K, then the second element is P and we can only fit two PKPs. Hence, the sixth element is P and the second is K. From there, the eighth column falls out and we get the following,

Step 5

The second row has three KPKs and there is only one way to achieve this. The 0 in the fourth column then gives us an extra P there.

Step 6

Now look at the second column and suppose the third or seventh elements are P. Then there would be no way to fit three PKPs in this column. These must both then be Ks and in fact we get the middle part of the second column immediately. Now, look at the 0 in the seventh row, we get an additional K and P so we end up with the following

Step 7

Now looking at the fifth column, we note that fitting three PKPs in is very restrictive. If one doesn't show up at the beginning then we cannot fit three in and the same for the end. Then looking at both the first and last row (same so far), we can only fit in two KPKs if the fourth and sixth elements are K. This leads to the following

Step 8

Looking back to the first column, PKP must occur at the beginning and at the end to fit three in overall. This allows us to complete the first and last rows.

Step 9

Some more entries are forced in the third and sixth columns by the presence of two PKPs and then the fifth and sixth rows are forced by requiring we fit two (more) KPKs into both and we are done.

• Great explanation, very well done! :D Sep 3, 2021 at 0:59
• @athin Thank you, great puzzle! Sep 4, 2021 at 12:46