Jason,

Much appreciated, you've almost written more code to test this than I will =
have in=20
the application~!

I persisted with Excel and produced a list of 1M results and did a sorted c=
ount by=20
checksum value. Side by side it agrees with your results perfectly~! Excel =
is a little=20
slow when it's working with 10^6 rows, copy and paste keeps it busy for 10-=
20s,=20
then about 5s to recalculate the whole sheet... so it definitely took a lit=
tle longer than=20
your C programs 1.8s.

Yes, the modulo 256 makes the results "wrap around" in some weird places, b=
ut the=20
good news is 0xFF is not in the set of results so I can happily use that.

On 10 Dec 2017 at 23:28, Jason White wrote:

> Hello Brent,
>=20
> I'm no mathematician and I suspect an analytical solution would be
> nontrivial due to the modulo.
>=20
> However the problem is easily solved by writing a C program
> (attached). I have written a program that computes the checksum for
> every possible digit combination and writes the number of occurrences
> for each checksum into a table. I have also attached the result tables
> for the set of digits 0-9 (used to test the validity of the program)
> and for your set of 10 BCD-like digits.
>=20
> It would appear that the answer to your question is: no. The checksum
> 0xFF does not appear. Although many other numbers do show up.
>=20
> -Jason
>=20
> Below is a list of all checksums that appear a nonzero number of times.
>=20
> Checksum 0x0b: 2002
> Checksum 0x0c: 54747
> Checksum 0x0d: 4332
> Checksum 0x1a: 1287
> Checksum 0x1b: 53262
> Checksum 0x1c: 6062
> Checksum 0x29: 792
> Checksum 0x2a: 50877
> Checksum 0x2b: 8232
> Checksum 0x38: 462
> Checksum 0x39: 47712
> Checksum 0x3a: 10872
> Checksum 0x47: 252
> Checksum 0x48: 43917
> Checksum 0x49: 13992
> Checksum 0x56: 126
> Checksum 0x57: 39662
> Checksum 0x58: 17577
> Checksum 0x65: 56
> Checksum 0x66: 35127
> Checksum 0x67: 21582
> Checksum 0x68: 1
> Checksum 0x74: 21
> Checksum 0x75: 30492
> Checksum 0x76: 25927
> Checksum 0x77: 6
> Checksum 0x83: 6
> Checksum 0x84: 25927
> Checksum 0x85: 30492
> Checksum 0x86: 21
> Checksum 0x92: 1
> Checksum 0x93: 21582
> Checksum 0x94: 35127
> Checksum 0x95: 56
> Checksum 0xa2: 17577
> Checksum 0xa3: 39662
> Checksum 0xa4: 126
> Checksum 0xb1: 13992
> Checksum 0xb2: 43917
> Checksum 0xb3: 252
> Checksum 0xc0: 10872
> Checksum 0xc1: 47712
> Checksum 0xc2: 462
> Checksum 0xcf: 8232
> Checksum 0xd0: 50877
> Checksum 0xd1: 792
> Checksum 0xde: 6062
> Checksum 0xdf: 53262
> Checksum 0xe0: 1287
> Checksum 0xed: 4332
> Checksum 0xee: 54747
> Checksum 0xef: 2002
> Checksum 0xfc: 2997
> Checksum 0xfd: 55252
> Checksum 0xfe: 2997
>=20


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