With just 22 items being scattered around 64, it sounds to me like the
number of Permutations.

=FACT(64) - 1.26887E+89

all possible deployments of these 22 pieces (sets of 22 numbers)

Sounds like it could be Chess pieces, or maybe not.
We would need more info.
--
Dana DeLouis


"David Biddulph" <groups [at] biddulph.org.uk wrote in message
...
9E+37 if each of the 22 pieces are unique.
The OP didn't make it clear whether he wanted to distinguish between 8
white pawns, or between 2 black rooks, or between 2 white bishops (with
the interesting complication that the OP said he didn't want to
distinguish between black & white squares, which would normally
distinguish the 2 white bishops).
Nor did he make it clear which 22 of the original 32 pieces he has.
--
David Biddulph

"joeu2004" wrote in message
...
Errata....

On Dec 25, 12:43 pm, I wrote:
There are about 8E+16 ways of arranging 22 pieces on an 8x8 board.

Actually, I think the number is 9E+37. Either way, it's a b-i-g
number.

On Dec 26, 10:38*am, "Dana DeLouis" wrote:
With just 22 items being scattered around 64, it sounds to me like the
number of Permutations.

=FACT(64) *- *1.26887E+89

There are "64 choose 22" ways of selecting 22 of the 64 squares on
which to place the pieces. It does not matter whether we choose those
squares in the order of 1,2,...,22 or 22,23,...1, for example. In
Excel, that would be COMBIN(64,22).

If the 22 pieces are distinct (I now believe they are not), there are
FACT(22) ways of ordering the pieces on each of the "64 choose 22"
combinations. You could multiply the two, or you could simply compute
PERMUT(64,22).

PERMUT(64,22).

You are absolutely correct. My mistake.
Thanks for the catch. :)
--
Dana

"joeu2004" wrote in message
...
On Dec 26, 10:38 am, "Dana DeLouis" wrote:
With just 22 items being scattered around 64, it sounds to me like the
number of Permutations.

=FACT(64) - 1.26887E+89

There are "64 choose 22" ways of selecting 22 of the 64 squares on
which to place the pieces. It does not matter whether we choose those
squares in the order of 1,2,...,22 or 22,23,...1, for example. In
Excel, that would be COMBIN(64,22).

If the 22 pieces are distinct (I now believe they are not), there are
FACT(22) ways of ordering the pieces on each of the "64 choose 22"
combinations. You could multiply the two, or you could simply compute
PERMUT(64,22).