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Office Applications and Entertainment, Magic Squares
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Attachment 16.1.6 |
About the Author
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Pairsums, Magic Constants, Center Elements, Variable Values {ai}:
| Pair |
MC3 |
Mid |
nVar |
Variables |
| 8450 |
12675 |
4225 |
9 |
169 |
529 |
1225 |
2209 |
4225 |
6241 |
7225 |
7921 |
8281 |
| 14450 |
21675 |
7225 |
9 |
289 |
1225 |
1681 |
5041 |
7225 |
9409 |
12769 |
13225 |
14161 |
| 31250 |
46875 |
15625 |
7 |
625 |
5329 |
7225 |
15625 |
24025 |
25921 |
30625 |
- |
| 33800 |
50700 |
16900 |
9 |
676 |
2116 |
4900 |
8836 |
16900 |
24964 |
28900 |
31684 |
33124 |
| 42050 |
63075 |
21025 |
9 |
25 |
841 |
14161 |
16129 |
21025 |
25921 |
27889 |
41209 |
42025 |
| 57800 |
86700 |
28900 |
9 |
1156 |
4900 |
6724 |
20164 |
28900 |
37636 |
51076 |
52900 |
56644 |
| 68450 |
102675 |
34225 |
9 |
1369 |
2401 |
13225 |
14161 |
34225 |
54289 |
55225 |
66049 |
67081 |
| 76050 |
114075 |
38025 |
9 |
1521 |
4761 |
11025 |
19881 |
38025 |
56169 |
65025 |
71289 |
74529 |
| 84050 |
126075 |
42025 |
9 |
529 |
1681 |
10609 |
24025 |
42025 |
60025 |
73441 |
82369 |
83521 |
| 97682 |
146523 |
48841 |
9 |
961 |
8281 |
14161 |
39601 |
48841 |
58081 |
83521 |
89401 |
96721 |
| 125000 |
187500 |
62500 |
7 |
2500 |
21316 |
28900 |
62500 |
96100 |
103684 |
122500 |
- |
| 130050 |
195075 |
65025 |
9 |
2601 |
11025 |
15129 |
45369 |
65025 |
84681 |
114921 |
119025 |
127449 |
| 135200 |
202800 |
67600 |
9 |
2704 |
8464 |
19600 |
35344 |
67600 |
99856 |
115600 |
126736 |
132496 |
| 140450 |
210675 |
70225 |
9 |
2809 |
7225 |
22801 |
58081 |
70225 |
82369 |
117649 |
133225 |
137641 |
| 168200 |
252300 |
84100 |
9 |
100 |
3364 |
56644 |
64516 |
84100 |
103684 |
111556 |
164836 |
168100 |
| 186050 |
279075 |
93025 |
9 |
289 |
3721 |
18769 |
60025 |
93025 |
126025 |
167281 |
182329 |
185761 |
| 211250 |
316875 |
105625 |
15 |
2401 |
4225 |
13225 |
30625 |
48841 |
55225 |
82369 |
105625 |
128881 |
| - |
156025 |
162409 |
180625 |
198025 |
207025 |
208849 |
- |
| 231200 |
346800 |
115600 |
9 |
4624 |
19600 |
26896 |
80656 |
115600 |
150544 |
204304 |
211600 |
226576 |
| 266450 |
399675 |
133225 |
9 |
1225 |
5329 |
78961 |
113569 |
133225 |
152881 |
187489 |
261121 |
265225 |
| 273800 |
410700 |
136900 |
9 |
5476 |
9604 |
52900 |
56644 |
136900 |
217156 |
220900 |
264196 |
268324 |
| 281250 |
421875 |
140625 |
7 |
5625 |
47961 |
65025 |
140625 |
216225 |
233289 |
275625 |
- |
| 284258 |
426387 |
142129 |
9 |
169 |
37249 |
41209 |
47089 |
142129 |
237169 |
243049 |
247009 |
284089 |
| 304200 |
456300 |
152100 |
9 |
6084 |
19044 |
44100 |
79524 |
152100 |
224676 |
260100 |
285156 |
298116 |
| 336200 |
504300 |
168100 |
9 |
2116 |
6724 |
42436 |
96100 |
168100 |
240100 |
293764 |
329476 |
334084 |
| 361250 |
541875 |
180625 |
15 |
49 |
7225 |
30625 |
42025 |
83521 |
108241 |
126025 |
180625 |
235225 |
| - |
253009 |
277729 |
319225 |
330625 |
354025 |
361201 |
- |
| etc. |
| 1445000 |
2167500 |
722500 |
15 |
196 |
28900 |
122500 |
168100 |
334084 |
432964 |
504100 |
722500 |
940900 |
| - |
1012036 |
1110916 |
1276900 |
1322500 |
1416100 |
1444804 |
- |
| etc. |
| 2442050 |
3663075 |
1221025 |
27 |
5329 |
24025 |
48841 |
134689 |
152881 |
207025 |
284089 |
354025 |
638401 |
| - |
654481 |
851929 |
990025 |
1117249 |
1221025 |
1324801 |
1452025 |
1590121 |
1787569 |
| 1803649 |
2088025 |
2157961 |
2235025 |
2289169 |
2307361 |
2393209 |
2418025 |
2436721 |
| etc. |
| 3251250 |
4876875 |
1625625 |
15 |
441 |
65025 |
275625 |
378225 |
751689 |
974169 |
1134225 |
1625625 |
2117025 |
| - |
2277081 |
2499561 |
2873025 |
2975625 |
3186225 |
3250809 |
- |
| etc. |
| 5780000 |
8670000 |
2890000 |
15 |
784 |
115600 |
490000 |
672400 |
1336336 |
1731856 |
2016400 |
2890000 |
3763600 |
| - |
4048144 |
4443664 |
5107600 |
5290000 |
5664400 |
5779216 |
- |
| etc. |
| 9031250 |
13546875 |
4515625 |
21 |
1225 |
37249 |
180625 |
765625 |
1050625 |
1540081 |
2088025 |
2706025 |
3150625 |
| - |
3352561 |
4515625 |
5678689 |
5880625 |
6325225 |
6943225 |
7491169 |
7980625 |
8265625 |
| 8850625 |
8994001 |
9030025 |
- |
| etc. |
| 9768200 |
14652300 |
4884100 |
27 |
21316 |
96100 |
195364 |
538756 |
611524 |
828100 |
1136356 |
1416100 |
2553604 |
| - |
2617924 |
3407716 |
3960100 |
4468996 |
4884100 |
5299204 |
5808100 |
6360484 |
7150276 |
| 7214596 |
8352100 |
8631844 |
8940100 |
9156676 |
9229444 |
9572836 |
9672100 |
9746884 |
| etc. |
| 13005000 |
19507500 |
6502500 |
15 |
1764 |
260100 |
1102500 |
1512900 |
3006756 |
3896676 |
4536900 |
6502500 |
8468100 |
| - |
9108324 |
9998244 |
11492100 |
11902500 |
12744900 |
13003236 |
- |
| etc. |
| 17701250 |
26551875 |
8850625 |
15 |
2401 |
354025 |
1500625 |
2059225 |
4092529 |
5303809 |
6175225 |
8850625 |
11526025 |
| - |
12397441 |
13608721 |
15642025 |
16200625 |
17347225 |
17698849 |
- |
| etc. |
| 21978450 |
32967675 |
10989225 |
27 |
47961 |
216225 |
439569 |
1212201 |
1375929 |
1863225 |
2556801 |
3186225 |
5745609 |
| - |
5890329 |
7667361 |
8910225 |
10055241 |
10989225 |
11923209 |
13068225 |
14311089 |
16088121 |
| 16232841 |
18792225 |
19421649 |
20115225 |
20602521 |
20766249 |
21538881 |
21762225 |
21930489 |
| etc. |
| 23120000 |
34680000 |
11560000 |
15 |
3136 |
462400 |
1960000 |
2689600 |
5345344 |
6927424 |
8065600 |
11560000 |
15054400 |
| - |
16192576 |
17774656 |
20430400 |
21160000 |
22657600 |
23116864 |
- |
| etc. |
| 29261250 |
43891875 |
14630625 |
15 |
3969 |
585225 |
2480625 |
3404025 |
6765201 |
8767521 |
10208025 |
14630625 |
19053225 |
| - |
20493729 |
22496049 |
25857225 |
26780625 |
28676025 |
29257281 |
- |
| etc. |
| 36125000 |
54187500 |
18062500 |
21 |
4900 |
148996 |
722500 |
3062500 |
4202500 |
6160324 |
8352100 |
10824100 |
12602500 |
| - |
13410244 |
18062500 |
22714756 |
23522500 |
25300900 |
27772900 |
29964676 |
31922500 |
33062500 |
| 35402500 |
35976004 |
36120100 |
- |
| etc. |
| 39072800 |
58609200 |
19536400 |
27 |
85264 |
384400 |
781456 |
2155024 |
2446096 |
3312400 |
4545424 |
5664400 |
10214416 |
| - |
10471696 |
13630864 |
15840400 |
17875984 |
19536400 |
21196816 |
23232400 |
25441936 |
28601104 |
| 28858384 |
33408400 |
34527376 |
35760400 |
36626704 |
36917776 |
38291344 |
38688400 |
38987536 |
| etc. |
| 43711250 |
65566875 |
21855625 |
15 |
5929 |
874225 |
3705625 |
5085025 |
10106041 |
13097161 |
15249025 |
21855625 |
28462225 |
| - |
30614089 |
33605209 |
38626225 |
40005625 |
42837025 |
43705321 |
- |
| etc. |
| 52020000 |
78030000 |
26010000 |
15 |
7056 |
1040400 |
4410000 |
6051600 |
12027024 |
15586704 |
18147600 |
26010000 |
33872400 |
| - |
36433296 |
39992976 |
45968400 |
47610000 |
50979600 |
52012944 |
- |
| etc. |
| 61051250 |
91576875 |
30525625 |
45 |
8281 |
133225 |
600625 |
693889 |
1221025 |
2053489 |
3367225 |
3822025 |
5175625 |
| - |
7102225 |
8532241 |
8850625 |
9541921 |
14115049 |
15960025 |
16362025 |
18292729 |
19280881 |
| 21298225 |
23804641 |
24750625 |
27931225 |
30525625 |
33120025 |
36300625 |
37246609 |
39753025 |
| 41770369 |
42758521 |
44689225 |
45091225 |
46936201 |
51509329 |
52200625 |
52519009 |
53949025 |
| 55875625 |
57229225 |
57684025 |
58997761 |
59830225 |
60357361 |
60450625 |
60918025 |
61042969 |
| etc. |
| 70805000 |
106207500 |
35402500 |
15 |
9604 |
1416100 |
6002500 |
8236900 |
16370116 |
21215236 |
24700900 |
35402500 |
46104100 |
| - |
49589764 |
54434884 |
62568100 |
64802500 |
69388900 |
70795396 |
- |
| etc. |
| 81281250 |
121921875 |
40640625 |
21 |
11025 |
335241 |
1625625 |
6890625 |
9455625 |
13860729 |
18792225 |
24354225 |
28355625 |
| - |
30173049 |
40640625 |
51108201 |
52925625 |
56927025 |
62489025 |
67420521 |
71825625 |
74390625 |
| 79655625 |
80946009 |
81270225 |
- |
| etc. |
| 87913800 |
131870700 |
43956900 |
27 |
191844 |
864900 |
1758276 |
4848804 |
5503716 |
7452900 |
10227204 |
12744900 |
22982436 |
| - |
23561316 |
30669444 |
35640900 |
40220964 |
43956900 |
47692836 |
52272900 |
57244356 |
64352484 |
| 64931364 |
75168900 |
77686596 |
80460900 |
82410084 |
83064996 |
86155524 |
87048900 |
87721956 |
| etc. |
| 92480000 |
138720000 |
46240000 |
15 |
12544 |
1849600 |
7840000 |
10758400 |
21381376 |
27709696 |
32262400 |
46240000 |
60217600 |
| - |
64770304 |
71098624 |
81721600 |
84640000 |
90630400 |
92467456 |
- |
| etc. |
| 104401250 |
156601875 |
52200625 |
17 |
8850625 |
12145225 |
19669225 |
22118209 |
24137569 |
31281649 |
36421225 |
46717225 |
52200625 |
| - |
57684025 |
67980025 |
73119601 |
80263681 |
82283041 |
84732025 |
92256025 |
95550625 |
- |
| etc. |