Let's expand the Chinese domino set

The Game Room
1

As a wee lad, I learned to play dominoes with the classic western double-six set. As I got older, I learned to play a number of different games with larger sets, most notably the double-twelve set as the usual choice for Mexican Train. Living in Asia for quite some time now, of course I’ve learned a few games witht the Chinese domino set.

The western set can be of any size, usually a double-six set (lightest domino is double-zero and heaviest is double-six) and an upper limit of double-n set. The formula for determining the number of dominoes in a set is ((n^2 + 3n + 2) / 2), where n is the highest doubled number. So, a double-zero set has one domino, a double-one set would has three dominoes, a double-six set has twentyeight dominoes, and a double-eighteen (evidently the largest commercially available set) has one hundred ninety dominoes.

The Chinese set only comes in one variety: double-six. The formula above does not work for that for two reasons: (1) there are no blanks in the Chinese set, and (2) one suit, called the civil suit is duplicated. Thus we have the following 32 dominoes:

  • Civil suit has two each of: 6-6, 1-1, 4-4, 1-3, 5-5, 3-3, 2-2, 5-6, 4-6, 1-6, 1-5
  • Military suit has one each of: 1-2, 1-4, 2-3, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6 and 4-5

So, how could this set be expanded to a higher double, all the way up to double-eighteen? I figure that the beginning is to determine what are the commanalities for the civil suit tiles? All of the doubles are in that suit, but the non-doubles are: 1-3, 1-5, 1-6, 4-6, 5-6. Why those particular non-doubles? If it’s random, then that means choosing a proportionate number of random tiles from the double-n set. But, I don’t want to just blithely declare it random. Is there some mathematics hidden in the traditional Chinese set’s civil series’ non-doubles and that’s why those are the tiles in that suit in addition to the doubles? Of coursse, the original double-six set’s civil suit’s dominoes must all be in the next higher double-n set’s civil suit and each successive expansion should only add two copies of one domino to the previous expansion’s civil suit.

Is this doable? I’m actually more concerned about the mathematics involved than in playing any games with this super-sized Chinese set, but expanding the rules for known Chinese games with the traditional set is also of some interest. First, I’d like to figure out the expansions.

Gee, I hope all of that’s clear. Let me know if it’s not.

2

Here’s the pattern I see in the civil suit in a double-n set:

  • All the doubles
  • The 1-odd
  • The large-6, where large > n/2
  • The 1-n

I don’t know enough about the Chinese games to know whether it’s better to make more duplicates of the civil suit or expand the definition to balance the set. (For that matter, there is exactly one thing I’ve learned about Chinese dominoes that isn’t mentioned above: the tiles use pips instead of Chinese characters.)

Ways to add more tiles to the civil suit could be:

  • Include all 1-x and x-n tiles
  • Add near-doubles: 1-2, 2-3, 3-4, …, (n-1)-n
  • Add 2-even tiles
  • Add large-(n-1) tiles

Do any of those strategies look like they would preserve the feel of the Chinese games while expanding the set size?

3

Sorry I didn’t get back to you until now. First, thanks for that effort. The whole post is great.

You got it! How did you see that pattern? There’s no way I could. As soon as I can, I’ll spend some time listing in a spreadsheet the full civil sets for sets up to double 18.

If one has to duplicate the civil suit, then one would have to duplicate the military suit also, so would one make a set with twice as many civil suits as military suits or a set with one more civil than military suits? For the original set, both of these choices turn out the same so it’s not definitely “wrong” whichever choice is made.

I like all of these suggestions. But I got confused on something. What’s the x standing in for? Oh, and I guess I’ll tweak the spreadsheet to see what the resulting sets look like with each of these suggestions alone or in combination with one, two, or all three of the others.

Honestly, I think so long as the civil suit with duplicated tiles, the feel of the original games* will still be there, but some will lose some interest due to the small number of duplicatee tiles if thte civil suit itself is not expanded as the entire set is expanded.

*I suppose some games would also need some slight tweaking given the ensuing size of the expanded sets. That tweak could be minor changes in the rules of play, or it could be in the number of players involved.

Again, thanks!

4

@Kimble

Now that the semester has ended, I’ve had an opportunity to work up a spreadsheet using the parameters you’ve discovered. As it turns out, if n is an odd number, then n/2 will, of course, generate .5 at the end. For that, I decided to round up (the usual rule in mathematics, I’m told). I also decided to go with just two copies of each Civil suit domino regardless of what n equals. This actually generates some interesting phenomena as it turns out.

Anyway, here is what I get for n=6, n=7, and n=8. Do you concur?

  • n=6
    Civil (two each of): 6-6, 1-1, 4-4, 1-3, 5-5, 3-3, 2-2, 5-6, 4-6, 1-6, 1-5
    Military (one each of): 1-2, 1-4, 2-3, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6, 4-5
    Total number of dominoes in set: 32

  • n=7
    Civil (two each of): 7-7, 7-4, 7-1, 6-6, 5-5, 5-1, 4-4, 3-3, 3-1, 2-2, 1-1
    Military (one each of): 7-6, 7-5, 7-3, 7-2, 6-5, 6-4, 6-3, 6-2, 6-1, 5-4, 5-3, 5-2, 4-3, 4-2, 4-1, 3-2, 2-1
    Total number of dominoes in set: 39

  • n=8
    Civil (two each of): 8-8, 8-4, 8-1, 7-7, 7-1, 6-6, 5-5, 5-1, 4-4, 3-3, 3-1, 2-2, 1-1
    Military (one each of): 8-7, 8-6, 8-5, 8-3, 8-2, 7-6, 7-5, 7-4, 7-3, 7-2, 6-5, 6-4, 6-3, 6-2, 6-1, 5-4, 5-3, 5-2, 4-3, 4-2, 4-1, 3-2, 2-1
    Total number of dominoes in set: 49

If this is correct, I’ll complete the calculations for all the other sets up to n=18. And I’m now curious what the series will be for the number of dominoes in each set. Thus far, I have 32, 39, 49. If we can determine the series requirement, then it might be fun to see what the total number of dominoes would be for n=100 or even higher. Same applies for number of Civil dominoes in each set and number of Military dominoes in each set.

By the way, I showed one of the Chinese teachers at my school the parameters you determined. He stared at it for a while, then said, “Wow. It is!” Evidently, nobody’s ever figured that out before or it’s just been lost to time and people just memorize the dominoes which are in which suit. I fully intend to put this into an escape room the students will be doing next semester.

Thanks!

5

I messed that one up. It should be:

  • n=8
    Civil (two each of): 8-8, 8-4, 7-7, 7-1, 6-6, 5-5, 5-1, 4-4, 3-3, 3-1, 2-2, 1-1
    Military (one each of): 8-7, 8-6, 8-5, 8-3, 8-2, 8-1, 7-6, 7-5, 7-4, 7-3, 7-2, 6-5, 6-4, 6-3, 6-2, 6-1, 5-4, 5-3, 5-2, 4-3, 4-2, 4-1, 3-2, 2-1
    Total number of dominoes in set: 48.

That’ll give the series I mentioned above as: 32, 39, 48.

I think the rest of my computations are correct.

6

I have to do this as a series of posts given Discourse’s limit on characters. You’ll have to forgive my formatting errors since I’ve had little (if any) practice (or success even) with Discourse formatting. Assuming my calculations are correct and I transcribed the results correctly, here is what I get for a set of size n (n from 1 to 18) using the parameters Kimble determined for the Civil suits. Of course, the Military suit is all those dominoes not in the Civil suit. The number 1 to the right of “Civil” and “Military” is to make it easier for me to sum the dominoes in each suit. You’ll notice I did not repeat each domino in the Civil suit (6-6, 6-6), but listed it just once (6-6), then accounted for the Civil suit being repeated by showing TOTAL as {Civil Suit total}*2+{Military Suit total}. It did occur to me to us 2 for the Civil suit in the domino list, but I had a few reasons for using 1, most notably seeing which tile would be duplicated and the total number of tiles in the set to be duplicated.

There results really are fascinating to me.

7
Column 1 Column 2 Column 3 Column 4 E F G H I J K L M N O P Q R S T U V W X Y Z AA AB AC AD AE AF AG AH AI AJ AK AL AM AN AO AP AQ AR
n=2 Suit Civil (Y=1) Military (Y=1) n=2 Suit Civil (Y=1) Military (Y=1) n=3 Suit Civil (Y=1) Military (Y=1) n=4 Suit Civil (Y=1) Military (Y=1) n=5 Suit Civil (Y=1) Military (Y=1) n=6 Suit Civil (Y=1) Military (Y=1) n=7 Suit Civil (Y=1) Military (Y=1) n=8 Suit Civil (Y=1) Military (Y=1) n=9 Suit Civil (Y=1) Military (Y=1)
1-1 Civil 1 2-2 Civil 1 3-3 Civil 1 4-4 Civil 1 5-5 Civil 1 6-6 Civil 1 7-7 Civil 1 8-8 Civil 1 9-9 Civil 1
1 0 2-1 Civil 1 3-2 Civil 1 4-3 Military 1 5-4 Military 1 6-5 Civil 1 7-6 Military 1 8-7 Military 1 9-8 Military 1
TOTAL 2 1-1 Civil 1 3-1 Civil 1 4-2 Civil 1 5-3 Civil 1 6-4 Civil 1 7-5 Military 1 8-6 Military 1 9-7 Military 1
3 0 2-2 Civil 1 4-1 Civil 1 5-2 Military 1 6-3 Military 1 7-4 Civil 1 8-5 Military 1 9-6 Military 1
TOTAL 6 2-1 Military 1 3-3 Civil 1 5-1 Civil 1 6-2 Military 1 7-3 Military 1 8-4 Civil 1 9-5 Civil 1
1-1 Civil 1 3-2 Military 1 4-4 Civil 1 6-1 Civil 1 7-2 Military 1 8-3 Military 1 9-4 Military 1
5 1 3-1 Civil 1 4-3 Military 1 5-5 Civil 1 7-1 Civil 1 8-2 Military 1 9-3 Military 1
TOTAL 11 2-2 Civil 1 4-2 Military 1 5-4 Military 1 6-6 Civil 1 8-1 Military 1 9-2 Military 1
2-1 Military 1 4-1 Military 1 5-3 Military 1 6-5 Military 1 7-7 Civil 1 9-1 Civil 1
1-1 Civil 1 3-3 Civil 1 5-2 Military 1 6-4 Military 1 7-6 Military 1 8-8 Civil 1
7 3 3-2 Military 1 5-1 Civil 1 6-3 Military 1 7-5 Military 1 8-7 Military 1
TOTAL 17 3-1 Civil 1 4-4 Civil 1 6-2 Military 1 7-4 Military 1 8-6 Military 1
2-2 Civil 1 4-3 Military 1 6-1 Military 1 7-3 Military 1 8-5 Military 1
2-1 Military 1 4-2 Military 1 5-5 Civil 1 7-2 Military 1 8-4 Military 1
1-1 Civil 1 4-1 Military 1 5-4 Military 1 7-1 Civil 1 8-3 Military 1
8 7 3-3 Civil 1 5-3 Military 1 6-6 Civil 1 8-2 Military 1
TOTAL 23 3-2 Military 1 5-2 Military 1 6-5 Military 1 8-1 Military 1
3-1 Civil 1 5-1 Civil 1 6-4 Military 1 7-7 Civil 1
2-2 Civil 1 4-4 Civil 1 6-3 Military 1 7-6 Military 1
2-1 Military 1 4-3 Military 1 6-2 Military 1 7-5 Military 1
1-1 Civil 1 4-2 Military 1 6-1 Military 1 7-4 Military 1
11 10 4-1 Military 1 5-5 Civil 1 7-3 Military 1
TOTAL 32 3-3 Civil 1 5-4 Military 1 7-2 Military 1
3-2 Military 1 5-3 Military 1 7-1 Civil 1
3-1 Civil 1 5-2 Military 1 6-6 Civil 1
2-2 Civil 1 5-1 Civil 1 6-5 Military 1
2-1 Military 1 4-4 Civil 1 6-4 Military 1
1-1 Civil 1 4-3 Military 1 6-3 Military 1
11 17 4-2 Military 1 6-2 Military 1
TOTAL 39 4-1 Military 1 6-1 Military 1
3-3 Civil 1 5-5 Civil 1
3-2 Military 1 5-4 Military 1
3-1 Civil 1 5-3 Military 1
2-2 Civil 1 5-2 Military 1
2-1 Military 1 5-1 Civil 1
1-1 Civil 1 4-4 Civil 1
12 24 4-3 Military 1
TOTAL 48 4-2 Military 1
4-1 Military 1
3-3 Civil 1
3-2 Military 1
3-1 Civil 1
2-2 Civil 1
2-1 Military 1
1-1 Civil 1
14 31
TOTAL 59
8
Column 1 Column 2 Column 3 Column 4 E F G H I J K L M N O P Q R S T U V W X
n=10 Suit Civil (Y=1) Military (Y=1) n=11 Suit Civil (Y=1) Military (Y=1) n=12 Suit Civil (Y=1) Military (Y=1) n=13 Suit Civil (Y=1) Military (Y=1) n=14 Suit Civil (Y=1) Military (Y=1)
10-10 Civil 1 11-11 Civil 1 12-12 Civil 1 13-13 Civil 1 14-14 Civil 1
10-9 Military 1 11-10 Military 1 12-11 Military 1 13-12 Military 1 14-13 Military 1
10-8 Military 1 11-9 Military 1 12-10 Military 1 13-11 Military 1 14-12 Military 1
10-7 Military 1 11-8 Military 1 12-9 Military 1 13-10 Military 1 14-11 Military 1
10-6 Military 1 11-7 Military 1 12-8 Military 1 13-9 Military 1 14-10 Military 1
10-5 Civil 1 11-6 Civil 1 12-7 Military 1 13-8 Military 1 14-9 Military 1
10-4 Military 1 11-5 Military 1 12-6 Civil 1 13-7 Civil 1 14-8 Military 1
10-3 Military 1 11-4 Military 1 12-5 Military 1 13-6 Military 1 14-7 Civil 1
10-2 Military 1 11-3 Military 1 12-4 Military 1 13-5 Military 1 14-6 Military 1
10-1 Civil 1 11-2 Military 1 12-3 Military 1 13-4 Military 1 14-5 Military 1
9-9 Civil 1 11-1 Civil 1 12-2 Military 1 13-3 Military 1 14-4 Military 1
9-8 Military 1 10-10 Civil 1 12-1 Civil 1 13-2 Military 1 14-3 Military 1
9-7 Military 1 10-9 Military 1 11-11 Civil 1 13-1 Civil 1 14-2 Military 1
9-6 Military 1 10-8 Military 1 11-10 Military 1 12-12 Civil 1 14-1 Military 1
9-5 Military 1 10-7 Military 1 11-9 Military 1 12-11 Military 1 13-13 Civil 1
9-4 Military 1 10-6 Military 1 11-8 Military 1 12-10 Military 1 13-12 Military 1
9-3 Military 1 10-5 Military 1 11-7 Military 1 12-9 Military 1 13-11 Military 1
9-2 Military 1 10-4 Military 1 11-6 Military 1 12-8 Military 1 13-10 Military 1
9-1 Civil 1 10-3 Military 1 11-5 Military 1 12-7 Military 1 13-9 Military 1
8-8 Civil 1 10-2 Military 1 11-4 Military 1 12-6 Military 1 13-8 Military 1
8-7 Military 1 10-1 Military 1 11-3 Military 1 12-5 Military 1 13-7 Military 1
8-6 Military 1 9-9 Civil 1 11-2 Military 1 12-4 Military 1 13-6 Military 1
8-5 Military 1 9-8 Military 1 11-1 Civil 1 12-3 Military 1 13-5 Military 1
8-4 Military 1 9-7 Military 1 10-10 Civil 1 12-2 Military 1 13-4 Military 1
8-3 Military 1 9-6 Military 1 10-9 Military 1 12-1 Military 1 13-3 Military 1
8-2 Military 1 9-5 Military 1 10-8 Military 1 11-11 Civil 1 13-2 Military 1
8-1 Military 1 9-4 Military 1 10-7 Military 1 11-10 Military 1 13-1 Civil 1
7-7 Civil 1 9-3 Military 1 10-6 Military 1 11-9 Military 1 12-12 Civil 1
7-6 Military 1 9-2 Military 1 10-5 Military 1 11-8 Military 1 12-11 Military 1
7-5 Military 1 9-1 Civil 1 10-4 Military 1 11-7 Military 1 12-10 Military 1
7-4 Military 1 8-8 Civil 1 10-3 Military 1 11-6 Military 1 12-9 Military 1
7-3 Military 1 8-7 Military 1 10-2 Military 1 11-5 Military 1 12-8 Military 1
7-2 Military 1 8-6 Military 1 10-1 Military 1 11-4 Military 1 12-7 Military 1
7-1 Civil 1 8-5 Military 1 9-9 Civil 1 11-3 Military 1 12-6 Military 1
6-6 Military 1 8-4 Military 1 9-8 Military 1 11-2 Military 1 12-5 Military 1
6-5 Military 1 8-3 Military 1 9-7 Military 1 11-1 Civil 1 12-4 Military 1
6-4 Military 1 8-2 Military 1 9-6 Military 1 10-10 Civil 1 12-3 Military 1
6-3 Military 1 8-1 Military 1 9-5 Military 1 10-9 Military 1 12-2 Military 1
6-2 Military 1 7-7 Civil 1 9-4 Military 1 10-8 Military 1 12-1 Military 1
6-1 Military 1 7-6 Military 1 9-3 Military 1 10-7 Military 1 11-11 Civil 1
5-5 Civil 1 7-5 Military 1 9-2 Military 1 10-6 Military 1 11-10 Military 1
5-4 Military 1 7-4 Military 1 9-1 Civil 1 10-5 Military 1 11-9 Military 1
5-3 Military 1 7-3 Military 1 8-8 Civil 1 10-4 Military 1 11-8 Military 1
5-2 Military 1 7-2 Military 1 8-7 Military 1 10-3 Military 1 11-7 Military 1
5-1 Civil 1 7-1 Civil 1 8-6 Military 1 10-2 Military 1 11-6 Military 1
4-4 Civil 1 6-6 Civil 1 8-5 Military 1 10-1 Military 1 11-5 Military 1
4-3 Military 1 6-5 Military 1 8-4 Military 1 9-9 Civil 1 11-4 Military 1
4-2 Military 1 6-4 Military 1 8-3 Military 1 9-8 Military 1 11-3 Military 1
4-1 Military 1 6-3 Military 1 8-2 Military 1 9-7 Military 1 11-2 Military 1
3-3 Civil 1 6-2 Military 1 8-1 Military 1 9-6 Military 1 11-1 Civil 1
3-2 Military 1 6-1 Military 1 7-7 Civil 1 9-5 Military 1 10-10 Civil 1
3-1 Civil 1 5-5 Civil 1 7-6 Military 1 9-4 Military 1 10-9 Military 1
2-2 Civil 1 5-4 Military 1 7-5 Military 1 9-3 Military 1 10-8 Military 1
2-1 Military 1 5-3 Military 1 7-4 Military 1 9-2 Military 1 10-7 Military 1
1-1 Civil 1 5-2 Military 1 7-3 Military 1 9-1 Civil 1 10-6 Military 1
15 40 5-1 Civil 1 7-2 Military 1 8-8 Civil 1 10-5 Military 1
TOTAL 70 4-4 Civil 1 7-1 Civil 1 8-7 Military 1 10-4 Military 1
4-3 Military 1 6-6 Civil 1 8-6 Military 1 10-3 Military 1
4-2 Military 1 6-5 Military 1 8-5 Military 1 10-2 Military 1
4-1 Military 1 6-4 Military 1 8-4 Military 1 10-1 Military 1
3-3 Civil 1 6-3 Military 1 8-3 Military 1 9-9 Civil 1
3-2 Military 1 6-2 Military 1 8-2 Military 1 9-8 Military 1
3-1 Civil 1 6-1 Military 1 8-1 Military 1 9-7 Military 1
2-2 Civil 1 5-5 Civil 1 7-7 Civil 1 9-6 Military 1
2-1 Military 1 5-4 Military 1 7-6 Military 1 9-5 Military 1
1-1 Civil 1 5-3 Military 1 7-5 Military 1 9-4 Military 1
17 49 5-2 Military 1 7-4 Military 1 9-3 Military 1
TOTAL 83 5-1 Civil 1 7-3 Military 1 9-2 Military 1
4-4 Civil 1 7-2 Military 1 9-1 Civil 1
4-3 Military 1 7-1 Civil 1 8-8 Civil 1
4-2 Military 1 6-6 Civil 1 8-7 Military 1
4-1 Military 1 6-5 Military 1 8-6 Military 1
3-3 Civil 1 6-4 Military 1 8-5 Military 1
3-2 Military 1 6-3 Military 1 8-4 Military 1
3-1 Civil 1 6-2 Military 1 8-3 Military 1
2-2 Civil 1 6-1 Military 1 8-2 Military 1
2-1 Military 1 5-5 Civil 1 8-1 Military 1
1-1 Civil 1 5-4 Military 1 7-7 Civil 1
19 59 5-3 Military 1 7-6 Military 1
TOTAL 97 5-2 Military 1 7-5 Military 1
5-1 Civil 1 7-4 Military 1
4-4 Civil 1 7-3 Military 1
4-3 Military 1 7-2 Military 1
4-2 Military 1 7-1 Civil 1
4-1 Military 1 6-6 Civil 1
3-3 Civil 1 6-5 Military 1
3-2 Military 1 6-4 Military 1
3-1 Civil 1 6-3 Military 1
2-2 Civil 1 6-2 Military 1
2-1 Military 1 6-1 Military 1
1-1 Civil 1 5-5 Civil 1
20 71 5-4 Military 1
TOTAL 111 5-3 Military 1
5-2 Military 1
5-1 Civil 1
4-4 Civil 1
4-3 Military 1
4-2 Military 1
4-1 Military 1
3-3 Civil 1
3-2 Military 1
3-1 Civil 1
2-2 Civil 1
2-1 Military 1
1-1 Civil 1
21 84
TOTAL 126
9
Column 1 Column 2 Column 3 Column 4 E F G H I J K L M N O P Q R S
n=15 Suit Civil (Y=1) Military (Y=1) n=16 Suit Civil (Y=1) Military (Y=1) n=17 Suit Civil (Y=1) Military (Y=1) n=18 Suit Civil (Y=1) Military (Y=1)
15-15 Civil 1 16-16 Civil 1 17-17 Civil 1 18-18 Civil 1
15-14 Military 1 16-15 Military 1 17-16 Military 1 18-17 Military 1
15-13 Military 1 16-14 Military 1 17-15 Military 1 18-16 Military 1
15-12 Military 1 16-13 Military 1 17-14 Military 1 18-15 Military 1
15-11 Military 1 16-12 Military 1 17-13 Military 1 18-14 Military 1
15-10 Military 1 16-11 Military 1 17-12 Military 1 18-13 Military 1
15-9 Military 1 16-10 Military 1 17-11 Military 1 18-12 Military 1
15-8 Civil 1 16-9 Military 1 17-10 Military 1 18-11 Military 1
15-7 Military 1 16-8 Civil 1 17-9 Civil 1 18-10 Military 1
15-6 Military 1 16-7 Military 1 17-8 Military 1 18-9 Civil 1
15-5 Military 1 16-6 Military 1 17-7 Military 1 18-8 Military 1
15-4 Military 1 16-5 Military 1 17-6 Military 1 18-7 Military 1
15-3 Military 1 16-4 Military 1 17-5 Military 1 18-6 Military 1
15-2 Military 1 16-3 Military 1 17-4 Military 1 18-5 Military 1
15-1 Civil 1 16-2 Military 1 17-3 Military 1 18-4 Military 1
14-14 Civil 1 16-1 Civil 1 17-2 Military 1 18-3 Military 1
14-13 Military 1 15-15 Civil 1 17-1 Civil 1 18-2 Military 1
14-12 Military 1 15-14 Military 1 16-16 Civil 1 18-1 Civil 1
14-11 Military 1 15-13 Military 1 16-15 Military 1 17-17 Civil 1
14-10 Military 1 15-12 Military 1 16-14 Military 1 17-16 Military 1
14-9 Military 1 15-11 Military 1 16-13 Military 1 17-15 Military 1
14-8 Military 1 15-10 Military 1 16-12 Military 1 17-14 Military 1
14-7 Military 1 15-9 Military 1 16-11 Military 1 17-13 Military 1
14-6 Military 1 15-8 Military 1 16-10 Military 1 17-12 Military 1
14-5 Military 1 15-7 Military 1 16-9 Military 1 17-11 Military 1
14-4 Military 1 15-6 Military 1 16-8 Military 1 17-10 Military 1
14-3 Military 1 15-5 Military 1 16-7 Military 1 17-9 Military 1
14-2 Military 1 15-4 Military 1 16-6 Military 1 17-8 Military 1
14-1 Military 1 15-3 Military 1 16-5 Military 1 17-7 Military 1
13-13 Civil 1 15-2 Military 1 16-4 Military 1 17-6 Military 1
13-12 Military 1 15-1 Civil 1 16-3 Military 1 17-5 Military 1
13-11 Military 1 14-14 Civil 1 16-2 Military 1 17-4 Military 1
13-10 Military 1 14-13 Military 1 16-1 Military 1 17-3 Military 1
13-9 Military 1 14-12 Military 1 15-15 Civil 1 17-2 Military 1
13-8 Military 1 14-11 Military 1 15-14 Military 1 17-1 Civil 1
13-7 Military 1 14-10 Military 1 15-13 Military 1 16-16 Civil 1
13-6 Military 1 14-9 Military 1 15-12 Military 1 16-15 Military 1
13-5 Military 1 14-8 Military 1 15-11 Military 1 16-14 Military 1
13-4 Military 1 14-7 Military 1 15-10 Military 1 16-13 Military 1
13-3 Military 1 14-6 Military 1 15-9 Military 1 16-12 Military 1
13-2 Military 1 14-5 Military 1 15-8 Military 1 16-11 Military 1
13-1 Civil 1 14-4 Military 1 15-7 Military 1 16-10 Military 1
12-12 Civil 1 14-3 Military 1 15-6 Military 1 16-9 Military 1
12-11 Military 1 14-2 Military 1 15-5 Military 1 16-8 Military 1
12-10 Military 1 14-1 Military 1 15-4 Military 1 16-7 Military 1
12-9 Military 1 13-13 Civil 1 15-3 Military 1 16-6 Military 1
12-8 Military 1 13-12 Military 1 15-2 Military 1 16-5 Military 1
12-7 Military 1 13-11 Military 1 15-1 Civil 1 16-4 Military 1
12-6 Military 1 13-10 Military 1 14-14 Civil 1 16-3 Military 1
12-5 Military 1 13-9 Military 1 14-13 Military 1 16-2 Military 1
12-4 Military 1 13-8 Military 1 14-12 Military 1 16-1 Military 1
12-3 Military 1 13-7 Military 1 14-11 Military 1 15-15 Civil 1
12-2 Military 1 13-6 Military 1 14-10 Military 1 15-14 Military 1
12-1 Military 1 13-5 Military 1 14-9 Military 1 15-13 Military 1
11-11 Civil 1 13-4 Military 1 14-8 Military 1 15-12 Military 1
11-10 Military 1 13-3 Military 1 14-7 Military 1 15-11 Military 1
11-9 Military 1 13-2 Military 1 14-6 Military 1 15-10 Military 1
11-8 Military 1 13-1 Civil 1 14-5 Military 1 15-9 Military 1
11-7 Military 1 12-12 Civil 1 14-4 Military 1 15-8 Military 1
11-6 Military 1 12-11 Military 1 14-3 Military 1 15-7 Military 1
11-5 Military 1 12-10 Military 1 14-2 Military 1 15-6 Military 1
11-4 Military 1 12-9 Military 1 14-1 Military 1 15-5 Military 1
11-3 Military 1 12-8 Military 1 13-13 Civil 1 15-4 Military 1
11-2 Military 1 12-7 Military 1 13-12 Military 1 15-3 Military 1
11-1 Civil 1 12-6 Military 1 13-11 Military 1 15-2 Military 1
10-10 Civil 1 12-5 Military 1 13-10 Military 1 15-1 Civil 1
10-9 Military 1 12-4 Military 1 13-9 Military 1 14-14 Civil 1
10-8 Military 1 12-3 Military 1 13-8 Military 1 14-13 Military 1
10-7 Military 1 12-2 Military 1 13-7 Military 1 14-12 Military 1
10-6 Military 1 12-1 Military 1 13-6 Military 1 14-11 Military 1
10-5 Military 1 11-11 Civil 1 13-5 Military 1 14-10 Military 1
10-4 Military 1 11-10 Military 1 13-4 Military 1 14-9 Military 1
10-3 Military 1 11-9 Military 1 13-3 Military 1 14-8 Military 1
10-2 Military 1 11-8 Military 1 13-2 Military 1 14-7 Military 1
10-1 Military 1 11-7 Military 1 13-1 Civil 1 14-6 Military 1
9-9 Civil 1 11-6 Military 1 12-12 Civil 1 14-5 Military 1
9-8 Military 1 11-5 Military 1 12-11 Military 1 14-4 Military 1
9-7 Military 1 11-4 Military 1 12-10 Military 1 14-3 Military 1
9-6 Military 1 11-3 Military 1 12-9 Military 1 14-2 Military 1
9-5 Military 1 11-2 Military 1 12-8 Military 1 14-1 Military 1
9-4 Military 1 11-1 Civil 1 12-7 Military 1 13-13 Civil 1
9-3 Military 1 10-10 Civil 1 12-6 Military 1 13-12 Military 1
9-2 Military 1 10-9 Military 1 12-5 Military 1 13-11 Military 1
9-1 Civil 1 10-8 Military 1 12-4 Military 1 13-10 Military 1
8-8 Civil 1 10-7 Military 1 12-3 Military 1 13-9 Military 1
8-7 Military 1 10-6 Military 1 12-2 Military 1 13-8 Military 1
8-6 Military 1 10-5 Military 1 12-1 Military 1 13-7 Military 1
8-5 Military 1 10-4 Military 1 11-11 Civil 1 13-6 Military 1
8-4 Military 1 10-3 Military 1 11-10 Military 1 13-5 Military 1
8-3 Military 1 10-2 Military 1 11-9 Military 1 13-4 Military 1
8-2 Military 1 10-1 Military 1 11-8 Military 1 13-3 Military 1
8-1 Military 1 9-9 Civil 1 11-7 Military 1 13-2 Military 1
7-7 Civil 1 9-8 Military 1 11-6 Military 1 13-1 Civil 1
7-6 Military 1 9-7 Military 1 11-5 Military 1 12-12 Civil 1
7-5 Military 1 9-6 Military 1 11-4 Military 1 12-11 Military 1
7-4 Military 1 9-5 Military 1 11-3 Military 1 12-10 Military 1
7-3 Military 1 9-4 Military 1 11-2 Military 1 12-9 Military 1
7-2 Military 1 9-3 Military 1 11-1 Civil 1 12-8 Military 1
7-1 Civil 1 9-2 Military 1 10-10 Civil 1 12-7 Military 1
6-6 Civil 1 9-1 Civil 1 10-9 Military 1 12-6 Military 1
6-5 Military 1 8-8 Civil 1 10-8 Military 1 12-5 Military 1
6-4 Military 1 8-7 Military 1 10-7 Military 1 12-4 Military 1
6-3 Military 1 8-6 Military 1 10-6 Military 1 12-3 Military 1
6-2 Military 1 8-5 Military 1 10-5 Military 1 12-2 Military 1
6-1 Military 1 8-4 Military 1 10-4 Military 1 12-1 Military 1
5-5 Civil 1 8-3 Military 1 10-3 Military 1 11-11 Civil 1
5-4 Military 1 8-2 Military 1 10-2 Military 1 11-10 Military 1
5-3 Military 1 8-1 Military 1 10-1 Military 1 11-9 Military 1
5-2 Military 1 7-7 Civil 1 9-9 Civil 1 11-8 Military 1
5-1 Civil 1 7-6 Military 1 9-8 Military 1 11-7 Military 1
4-4 Civil 1 7-5 Military 1 9-7 Military 1 11-6 Military 1
4-3 Military 1 7-4 Military 1 9-6 Military 1 11-5 Military 1
4-2 Military 1 7-3 Military 1 9-5 Military 1 11-4 Military 1
4-1 Military 1 7-2 Military 1 9-4 Military 1 11-3 Military 1
3-3 Civil 1 7-1 Civil 1 9-3 Military 1 11-2 Military 1
3-2 Military 1 6-6 Civil 1 9-2 Military 1 11-1 Civil 1
3-1 Civil 1 6-5 Military 1 9-1 Civil 1 10-10 Civil 1
2-2 Civil 1 6-4 Military 1 8-8 Civil 1 10-9 Military 1
2-1 Military 1 6-3 Military 1 8-7 Military 1 10-8 Military 1
1-1 Civil 1 6-2 Military 1 8-6 Military 1 10-7 Military 1
23 97 6-1 Military 1 8-5 Military 1 10-6 Military 1
TOTAL 143 5-5 Civil 1 8-4 Military 1 10-5 Military 1
5-4 Military 1 8-3 Military 1 10-4 Military 1
5-3 Military 1 8-2 Military 1 10-3 Military 1
5-2 Military 1 8-1 Military 1 10-2 Military 1
5-1 Civil 1 7-7 Civil 1 10-1 Military 1
4-4 Civil 1 7-6 Military 1 9-9 Civil 1
4-3 Military 1 7-5 Military 1 9-8 Military 1
4-2 Military 1 7-4 Military 1 9-7 Military 1
4-1 Military 1 7-3 Military 1 9-6 Military 1
3-3 Civil 1 7-2 Military 1 9-5 Military 1
3-2 Military 1 7-1 Civil 1 9-4 Military 1
3-1 Civil 1 6-6 Civil 1 9-3 Military 1
2-2 Civil 1 6-5 Military 1 9-2 Military 1
2-1 Military 1 6-4 Military 1 9-1 Civil 1
1-1 Civil 1 6-3 Military 1 8-8 Civil 1
25 111 6-2 Military 1 8-7 Military 1
TOTAL 161 6-1 Military 1 8-6 Military 1
5-5 Civil 1 8-5 Military 1
5-4 Military 1 8-4 Military 1
5-3 Military 1 8-3 Military 1
5-2 Military 1 8-2 Military 1
5-1 Civil 1 8-1 Military 1
4-4 Civil 1 7-7 Civil 1
4-3 Military 1 7-6 Military 1
4-2 Military 1 7-5 Military 1
4-1 Military 1 7-4 Military 1
3-3 Civil 1 7-3 Military 1
3-2 Military 1 7-2 Military 1
3-1 Civil 1 7-1 Civil 1
2-2 Civil 1 6-6 Civil 1
2-1 Military 1 6-5 Military 1
1-1 Civil 1 6-4 Military 1
26 127 6-3 Military 1
TOTAL 179 6-2 Military 1
6-1 Military 1
5-5 Civil 1
5-4 Military 1
5-3 Military 1
5-2 Military 1
5-1 Civil 1
4-4 Civil 1
4-3 Military 1
4-2 Military 1
4-1 Military 1
3-3 Civil 1
3-2 Military 1
3-1 Military 1
2-2 Civil 1
2-1 Military 1
1-1 Civil 1
27 144
TOTAL 198