## Total number of checkers positions…

I might actually get to constructing an endgame database for checkers sometime soon. To start, I decided to try to write code to reproduce the table that appears in Schaeffer’s paper on solving checkers. It basically is just a five nested loop that computes a big sum of some fairly obvious combinatorial terms. So, I coded it up in python, and ran it. It produced the numbers I was expecting, but slowly. Really slowly. Unacceptably slowly. Like well over an hour before I killed it.

Part of the code computes the binomial coefficients. I put in some code to memoize those numbers (don’t recalculate, just look them up in a dictionary if you’ve computed them before). Bam! 2 seconds later, and I had the following table.

``` N     possible positions
------------------------------
1                         120
2                       6,972
3                     261,224
4                   7,092,774
5                 148,688,232
6               2,503,611,964
7              34,779,531,480
8             406,309,208,481
9           4,048,627,642,976
10          34,778,882,769,216
11         259,669,578,902,016
12       1,695,618,078,654,976
13       9,726,900,031,328,256
14      49,134,911,067,979,776
15     218,511,510,918,189,056
16     852,888,183,557,922,816
17   2,905,162,728,973,680,640
18   8,568,043,414,939,516,928
19  21,661,954,506,100,113,408
20  46,352,957,062,510,379,008
21  82,459,728,874,435,248,128
22 118,435,747,136,817,856,512
23 129,406,908,049,181,900,800
24  90,072,726,844,888,186,880
------------------------------
500,995,484,682,338,672,639

```

## Another satellite recording…

I heard via the amsat-bb mailing list that RS-22 was still transmitting telemetry, but might be interrupted by low batteries during eclipse period. I haven’t tried to listen to any Russian satellites, so I thought I’d give it a try. My satellite prediction software yielded this data for this morning’s pass:

```RS-22 will be visible from grid CM87ux starting in 00:00:26 at 17:39:54
17:39:54  +0.1° 178.2° ? 12.7°N 121.5°W - AOS
17:40:00  +0.4° 178.4° ? 13.0°N 121.6°W -
17:41:00  +4.4° 180.3° ? 16.6°N 122.4°W -
17:42:00  +9.3° 182.9° ? 20.3°N 123.2°W -
17:43:00 +15.3° 186.7° ? 23.9°N 124.1°W -
17:44:00 +23.5° 192.9° ? 27.5°N 124.9°W -
17:45:00 +34.8° 204.8° ? 31.1°N 125.9°W -
17:46:00 +48.2° 231.5° ? 34.8°N 126.8°W -
17:46:39 +52.1° 261.9° ? 37.1°N 127.5°W - MAX
17:47:00 +50.5° 278.9° ? 38.4°N 127.9°W -
17:48:00 +38.1° 311.1° ? 42.0°N 129.0°W -
17:49:00 +26.0° 325.2° ? 45.6°N 130.2°W -
17:50:00 +17.3° 332.4° ? 49.2°N 131.6°W -
17:51:00 +10.9° 336.7° ? 52.7°N 133.1°W -
17:52:00  +5.9° 339.6° ? 56.3°N 134.9°W -
17:53:00  +1.7° 341.7° ? 59.8°N 137.0°W -
17:53:28  +0.0° 342.5° ? 61.5°N 138.1°W - LOS
```

So, I fired up my FT-817 and my digital voice recorder, wandered outside, and sure enough, picked it up easily. I recorded a bunch of it, and about 2/3 of the way through, realized i had my cables misrouted and I wasn’t actually recording. I shuffled quickly, and got a few code groups as it was Doppler shifting away.

RS-22 Telemetry (trimmed)