No matter what you cut, it works perfectly

[Barticle]

(The title is a browser mistranslation, used here for my own amusement - although it still makes sense.)

I found this puzzle while looking up something on Japanese Wikipedia.

You have an incomplete closed hand without any kongs and have just drawn your next tile to give you fourteen.

What hands would allow you to discard any tile and always be Yakuman Tenpai? (standard Japanese rules apply)

The page gives only two solutions, although there are two versions of one and many of the other.

Can you find one or both?

[Ozball]

Quick clarification... is the assumption that you're not in tenpai before your draw? or is being in tenpai allowed? (and the tsumo does not complete the hand)

[Barticle]

The solutions don't specify which tile you just drew, but in both cases the hand was Tenpai regardless of the tile.

Your hand remains incomplete after the draw, but every possible discard leaves you one away from a Yakuman.

(The original heading on Wikipedia includes the words Yakuman and Tenpai, but they were lost in translation.)

BTW that one solution with two versions could also have a third depending on whether or not a certain tile is required.

Just wanted to be clear, but it might even count as a hint.

[or2az]

I didn't get much sleep last night thinking about this.
It didn't help. Lets see if I understand this correctly.
I have a closed tenpai hand, probably for a yakuman.
I draw a tile. It's not the winner. A piece of junk.
I can now discard any tile in my hand, even keeping that piece of junk, and I will still be tenpai for a yakuman.
Wow, I can't see how that is even possible.
I tried every yakuman, even the optional ones.
I can't wait to be surprised.......but at least I won't lose any more sleep.

[Barticle]

Yes, you can discard any one of your fourteen tiles and always be Tenpai for a Yakuman... or two double Yakuman.

(That's a good hint for the other solution.)

These are standard Yakuman hands, none of the exotic local rules I enjoy.

I didn't say that I was going to give the answers.

(I will, but not until after the weekend. If your insomnia becomes critical, I can send you the answers!)

[Ozball]

Hmm ok, will take another crack at this shortly and see if I can come up with anything before the answers are posted.

EDIT: Ok some of my thoughts.

There seem to be a few sticking points:

• Being able to draw ANY tile and have it stick to the hand (and not go back in shanten)
• Being in Yakuman Tenpai, drawing a tile that DOESN'T complete the hand, but is still able to stick to the hand (Which probably means a shift in yakuman)
  One example of the point above that would work otherwise is:
  Tsumo:
  Technically the above satisfies the whole "Discard anything and be in Yakuman Tenpai", but in Drawing the White Dragon you've already completed the hand, so I believe that disqualifies it. You can in theory discard any of the tiles even if you draw something that's not the white dragon, and still have a Yakuman, but you move back in shanten if you discard anything other than the White Dragon or the Tile you drew.
  Example:
  Tsumo:
• I'm working on the assumption of a shift between Suuankou, and probably Dai/Shosuushi, or possibly Daisangen, these also allow for Tsuiisou to apply as well, but the problem lies with how you manage to move forward if you draw a non-honour, discard something other than the non-honour and still stay in tenpai

[Barticle]

It's past midnight here, but I'll wait until it's properly Monday after I've slept!

You should know now from the hints which Yakuman hands to use.

One last clarification and hint for the first solution:

Specifying a hand that's closed and without kongs was just a way of saying you have exactly fourteen tiles and none are locked in sets.

However I could've said that you have no declared kongs...

[Ozball]

One last clarification and hint for the first solution:

Specifying a hand that's closed and without kongs was just a way of saying you have exactly fourteen tiles and none are locked in sets.

However I could've said that you have no declared kongs...

I was thinking of being cheeky and claiming Suukantsu and saying that technically anything you draw you can discard any other tiles and still be in tenpai, but that's only because you only have 1 single tile left you're waiting on (Naked Tanki wait), and it wouldn't technically satisfy the "Discard any of the 14 tiles in your hand" part.

[Barticle]

Still effectively Sunday night here.

The answer would've been evident if the puzzle was "You have eighteen tiles and can discard any of two."

The four wind triplets are correct so you're almost there. The solutions are not complete hands. You can switch between two very similar Yakuman.

The kongs hint was for the other solution with two/three variants and the Yakuman that sometimes requires a specific tile.

The winds solution has 45 valid variants in total I think.

[Barticle]

So we're looking for incomplete hands of fourteen loose tiles where you can discard any of those tiles for Yakuman Tenpai.

(The puzzle does not concern your latest draw - you've already drawn a tile to give you fourteen - but, for any of the possible solutions, you must've always been Yakuman Tenpai regardless of which tile in that hand you just drew, because discarding your Tsumo must leave you Yakuman Tenpai too. The drawn tile didn't complete your hand but it must still be useful because it forms part of your ready hand if you now discard any other tile.)

I had effectively confirmed the windy solution already. You have four wind triplets and you can't have a pair too since that would complete the hand. You need something that gives a ready hand if you discard a wind tile so you want any two suit tiles that can form a sequence together (a Tātsu).

If you discard any wind, you're Tenpai for Little Four Winds.

If you discard either suit tile, you're Tenpai for Big Four Winds stacked with Four Concealed Triplets on a Pair Wait. (two double Yakuman)





The other solution involves All Green - which optionally may or may not require the green dragon - and uses two undeclared quads.

If you discard any tile, you're always waiting on a 3 to complete the Yakuman.

(For the two variants with a 666 triplet - if you discard a 2, you can also complete a non-Yakuman hand with a 5.)





(if green drags not required)

I found the puzzle on the Wikipedia page for All Green:

https://ja.wikipedia.org/wiki/%E7%B7%91 ... 1%E3%82%A4