## help on an ancient accounting tablet?

Hi all, I hope this long post is ok, and that some of you find it interesting!

This series of numerical entries below is from a clay tablet I am working on. They are recorded not as numbers but as various units that bundle, in a bisexigesimal system - I have put them all in terms of one of the smaller signs in the system, so that "420" for example, means "420 units X". The unit chosen was not arbitrary but may have held meaning conceptually - it is believed to be approximately 1 litre of grain, the amount of a daily 'ration' in the ancient near east. The numerical system and bundling principles are well-established and have been confirmed in tablets by scholars for 20 years. The tablet is a list of approximately 117 non-numerical entries (which are not yet deciphered) each followed by a numerical entry, then the end of the text consists of 3 summary entries.

I am a historian, and not particularly mathematically inclined, so I think it's a good idea to throw this out and see what kind of numerical patterns you might find. At present, no particular reason is known for the ordering of entries on this tablet, and the variations in sizes are strange in the context of rations - which is why I'm looking for other, numerical relationships between the various entries that might hint at the content.

Some of the entries are not certain either because of obscuration on the tablet, or because some of the numerical signs are sometimes confused with a non-numerical signs - this also makes the number of entries imprecise.

It is also important to know that at the 'end' in a separate space from the main text on the tablet, three numerical entries are listed. The second seems to be a total of all the entries listed in the text (allowing for the damaged areas) and the third, approximately (though frustratingly not exactly) thirty percent of that second entry. It is currently assumed that the numerical entries all refer to the same product - probably barley- being counted in capacity measures, but this is not certain.

From a purely numerical point of view, what do you see? Do the amounts seem to have any interesting relationships with eachother, and can you spot any major patterns in the ordering?

entry #/// numerical entry (in units of x)
1) NONE
2) 90 (it is unclear whether these signs are part of the same numerical system as the remainder of the entries)
3) 630
4) 90
5) 27
6) 4,320
7) 12
8) 479.5
9) 90
10) 60
11) 60
12) 60
13) 60
14) 60
15) 370.5
16) 210
17) 15
18) 46
19) 41
20) 53.5
21) 28
22) 5
23) 72
24) 127
25) 14
26) 15
27) 1
28) 57
29) 21.5
30) 4
31) 4
32) 15
33) 15
34) 11
35) 59
36) 15
37) 218
38) 11
39) 5
40) 10
41) 8
42) 1,215.5
43) 7
44) 273
45) 1,891
46) 83.5
47) 90
48) 210
49) 16.5
50) 27
51) 5.5
52) 16
53) 354
54) 101
55) 72
56) 2,753.25
57) 504
58) 222
59) 114.75
60) 904.75
61) 819.25
62) 39.5
63) ?
64) 114
65) 21
66) 9
67) 15.5
68) 3
69) 16.5
70) 16
71) 121.5
72) 740
73) 30
74) 8
75) 123.5
76) 18
77) 9
78) 3
79) 9
80) 42
81) 2,073
82) 465
83) 199
84) 630
85) ? (at least 60)
86) ?
87) ? (at least 450)
88) 30
89) 18
90) 90
91) 381.5
92) 57.2
93) 34
94) ? (at least 1,920)
95) .5
96) 739
97) 13
98) 24 (?)
99) 18
100) ?
101) 66
102) 72 (?)
103) 8.5
104) 30
105) 66
106) 22
107) ?
108) ?
109) ? (at least 18)
110) ?
111) 120
112) 4,917 *perhaps up to 180 more
113) ? (at least 4,140)
114) ? (at least 360, almost certainly not much more)
115) 300
116) 90
117) ? (at least 330, probably not much more)

SUMMARY ENTRIES:

1) 90 (unclear if these signs are part of the same numerical system - see entry 2 at the beginning)
2) 36,234.5
3) 10,500 (break leaves small chance that it's rather 10,680)