Total Invisible: The fairy piece Total Invisible is a piece which stands somewhere on the board, but whose color, identity and whereabouts are not known. The real identity of Total Invisible is any ordinary piece (including K if there is no K on the board). It is assumed that the initial position and the sequence of moves must be legal after the true identity of every Total Invisible is revealed. After all aspects of a Total Invisible are revealed, it becomes visible and turns into an ordinary piece. In an initial position, only the total number of Total Invisibles is given. (see Sake Tourney 2018 Announcement | Award)
White Ke1 TIf1 TIh8 TIg3 TIa1 TIc3
Black Kg4 Pf4h3
Neutral Qh1 Pg2
h#2.5 2 solutions (1+3+2)
4 Total Invisibles
{JV: On the diagram Total Invisibles remain invisible}
1...nQh1-g1 {means there is an Invisible on f1,
which is not bRf1/bQf1
} 2.nQg1-c5 0-0-0 {TId1=wR and there is an Invisible between wKc1 and nQc5,
but it is not bR or bQ, neither bTIc2, bSc3, bBc3.
} 3.f4*g3 {the fourth Invisible is captured on g3
} Rd1-d4# {none of the remaining Invisibles (TIf1 and TIc3/c4) can prevent
the mate by the white Rook
The Total Invisibles of the first solution:
wRa1, wTIg3, TIf1, TIc2/c3/c4
}
1...TIh8*h3 {the first two Invisibles are partially identified:
wTIh3 and one TIf1 or TIg1
} 2.nPg2*f1=nR+ nRf1-f3 {means TIf1 has been captured and there is
another Invisible on g1, but not bR/bQ
} 3.f4*g3 {the fourth Invisible was on g3 and has just been captured
} TIh3*g3=R {the only Invisible that can capture on g3 is TIh3 because TIg1
is pinned hence TIh3=wR!
The Total Invisibles of the second solution:
wR somewhere on the h-file capturing bPh3, wTIf1, wTIg3, TIg1}
The solutions are C+ by Popeye 4.83, which is not 100% trustworthy for Total Invisibles.
Hopefully they will offer some fun for solvers. (Author)
As there are neutral pieces on the board, the TIs may be neutral (why not?) and then second solution does not work, as the final TI may be a neutral rook (not a white one).
I have published other originals with Total Invisibles in Problem Paradise 86, Apr-Jun. 2019 and it was then already mentioned that “none of the Total Invisibles can be neutral.”
My concise definition of a Total Invisible would be the following:
“A white or black orthodox piece that stands somewhere on the board, but whose color, identity and whereabouts are not known. The initial position and sequence of moves of the solution must be legal. After all aspects of a Total Invisible are revealed, it becomes visible and turns into an ordinary piece.”
If you allow the Invisibles to be also neutral, then you need more moves to identify the White Invisibles that can give mate and exclude the neutral Invisibles that can prevent mate.
The solutions would be more diluted and would lose most of their charm.
Longer solutions would also mean more cooks, all the more so as Popeye doesn’t check problems with neutral Invisibles and can’t help you.
Thomas Maeder
January 3, 2021 22:08
BAD NEWS!
Testing problem 1572 with Popeye (and vice versa!) revealed (pun intended) a number of bugs in the Popeye implementation of TotalInvisibles.
For this problem, Popeye now also finds: 1…0-0-0 2.nPg2*f1=nQ nQf1*f4 3.nQf4-e5 Rd1-d4 # other TIs: g1(not Q or R), e3 (b[SP] or w[QRBP]) 1…nQh1-g1 2.f4*g3 0-0-0 3.nQg1-c5 Rd1-d4 # alternative move order for 1st solution
No.1463 
As there are neutral pieces on the board, the TIs may be neutral (why not?) and then second solution does not work, as the final TI may be a neutral rook (not a white one).
Perhaps it should be stipulated that as only neutral pawn and queen are there the TI can only be that, not a neutral rook !!
> the TIs may be neutral (why not?)
Obviously because I won’t program them 🙂
I have published other originals with Total Invisibles in Problem Paradise 86, Apr-Jun. 2019 and it was then already mentioned that “none of the Total Invisibles can be neutral.”
My concise definition of a Total Invisible would be the following:
“A white or black orthodox piece that stands somewhere on the board, but whose color, identity and whereabouts are not known. The initial position and sequence of moves of the solution must be legal. After all aspects of a Total Invisible are revealed, it becomes visible and turns into an ordinary piece.”
If you allow the Invisibles to be also neutral, then you need more moves to identify the White Invisibles that can give mate and exclude the neutral Invisibles that can prevent mate.
The solutions would be more diluted and would lose most of their charm.
Longer solutions would also mean more cooks, all the more so as Popeye doesn’t check problems with neutral Invisibles and can’t help you.
BAD NEWS!
Testing problem 1572 with Popeye (and vice versa!) revealed (pun intended) a number of bugs in the Popeye implementation of TotalInvisibles.
For this problem, Popeye now also finds:
1…0-0-0 2.nPg2*f1=nQ nQf1*f4 3.nQf4-e5 Rd1-d4 #
other TIs: g1(not Q or R), e3 (b[SP] or w[QRBP])
1…nQh1-g1 2.f4*g3 0-0-0 3.nQg1-c5 Rd1-d4 #
alternative move order for 1st solution