The 97 rational numbers 49/1, 49/2, 49/3, ..., 49/97 are written on a blackboard.
Two of the above numbers X and Y are chosen and replaced by X*Y-X-Y+1.
The procedure is repeated until a single number Z(say) remains on the board.
Determine the possible values of Z.
Just a sampling of 500 random orders of choosing X and Y:
The first three are shown in reduced fraction form and then decimal approximation. The rest in decimal approximation only:
-5629147602246762611999151041054972895968082513425702767009904108419649069385966785942833973741837409424439 / 122291701296739550370520982444255356529231588154516983574201535314445057459016706293760000000000000000
-46030.4954674536261757832
-24993592060268030372035981447648398475390214249325248488448838384912539200228014850877360213535004373525390622278603 / 339407448858212932326926075237282336208706706719009258584775150304437150556340948527763947520000000000000000
-73638902.5766758420055949239
646825480953238021935528325601345660437323340819754685455817040110189432825948410409512662635901 / 2444486425525641814595177563038121259771287169215680218270008413809222094097376870400000000000
264.6058796641303120332
5665.8435227450742633151
-2334740.5313735009483060006
-1007697.8071182154723195164
89367.5933190029185782525
12831.2997812900406818932
66966.5166231520201080866
-25835.7539877985556648125
-27473957.0406343723116270364
-4936276.2524156035832128253
39125.2056949602033811891
1.5726741157581100483
19479.5999179823068140442
14.3912986348515164264
45217747.8209651351620429276
824554.1616068471151085079
58568.6491810818207714188
42187938.692144646669529601
-13074.8579470878413918782
-12.7574679296110474587
-1.1869915289956849667
-1620920.1637422935423606922
695769.3458893459415582955
-3282689.6253197132774312769
100558854.3434294795854523157
-4179.4740580639671372842
-28.7509506648072172484
61755.6224726268719827176
20554.0334204905171807147
2401273.430714953617969701
35949.2671731863290221975
-93.0401999966624246492
22665682.4305884107804334743
-58.851671596380972956
-1860.0527473074504858483
3271710.9585311251372231169
230.0255605276647445577
10171.6065273780202407107
-8437493.0208185744045816994
3962326.5715130149305830402
9.1411204677110455372
-404151.6335765372988930162
-7036.3905927955505320752
2502.4222779666638091329
-1104.7080223980518042443
-44169.4288643376838250444
596807.4252943982500011547
6717.1544080070266688553
-1542.9146253828449438266
-41329.1298604929340950853
-9661.2259332823707352876
-1304895.315084682875946667
262.3984438577160110517
2.5593271921875522598
6433631.6887761606465279816
-3159928.5271115782009069089
-25517068.9137354153990662204
-156.0498045161489457823
287667.2637727920909775276
17.8414008033859352929
-145059.0150470665838703557
-8981.606178242012404225
1682.6733941412253770128
-5501747.6333367272360257521
21981.9909972238046836881
15.6829007815328385766
705.3329659494951042847
21968.0868786169622062844
9974.1164124951330315811
-327.8049163847490643242
127.6166954511039912589
-33408.5272449438748685561
-6694918.0201423076423249166
-17275.7519357893631427257
7108.1837366074316004601
-66562.7632801364722612802
4434.3748108140031440689
7167.4026048228512028982
41905.5727466949126946767
9272.2635442721349910511
2.5401644343144787569
28669.4672271420948336358
-352.4313765951127081145
5706.2539705471713104926
-25171.7422054918751985346
353367.4483635912635841777
23390.7431744714463493819
9.5890132817979788885
3068.5142668443104453166
-5853636.4200415317094429339
21411.6433431800244069835
0.0115284065001786156
-236614258.9632248208772005351
-3.60553674296413495
20863.1676756828154767852
-298453.2723194484108219179
0.0236432666557713765
-75738.3820178657084150459
2120923.2603835074775882656
-2781279.9227836782523955406
2947.6864218223183595743
4436693.2557545193051672349
120.808712439909653307
77203.313829329154805412
-43388.1205447839702904366
-67.696654181815951597
-108.1968881640574125993
372.3025713003129662719
-713922.9181446290433110731
-6581.7809602058376846876
11022.7730865459230192635
2129.2791273961776385601
1778043.0757028440743221812
939.7903245784495211845
537095.8098036592285420626
-20.0289494222332623204
-26542519.2330294772889920382
-9101.640559046452106764
-928152.7034177257565724874
-3521.0488068196339219331
5101.9386691109924167213
-67980.81487395121207069
248938.5549164320133105377
8923.2198636841565369668
6088463.2065283260384795249
216.8102565771600559786
-30844.2253968118053247109
81.1514348904992074834
23.6753058086552569625
-0.3775594583508806716
26.2427882388022395544
-107.1465195302979356516
9456561.3548581922041978711
-81378.0378407623300766959
-7256.8536520080017485964
-1186213.6043950941579083066
-90148.6631477834247852282
-249.442588474698919545
111448572.7955876538885025061
11173.2390201282191818055
3727.0392618967968222177
-68158.6770565025431753385
73026.6366986505916685317
-1482.0736419725597810153
-6.4521439876334922285
-152232.1907341079700628169
-126.5417389383835585185
-1652671.5156729779540849399
11653497.5496699860743650652
-20113924.9458732078230986532
891184.7199831918795021601
54232139.2831722978029515659
-20767.451639159935037211
54305.8001252654103964016
-73829.0765743975708004794
1035293159.9959051972736137986
1563591.6204049880259732447
-1970.175300876659581025
33895.5655786131623270193
-310213.9737570907016183837
25803.1266956491905604037
-3565.2306450145611073306
-9149.5592477420583920725
85.7573629195304616311
555.0527142972904172486
-5115246.6013512382486379003
-32649.2353555609828095034
15.3097312828517983532
-209700.5866357440240757336
117164.2174355344928674463
-59.2864409859628552125
4911392.8679338875034040202
51007971.852087485643234786
0.4195672969573884905
-2527.4333082077395461857
-1905.6906700155040216638
440249.4393801663569028987
760373.5062597025277420723
-1.7947545162006545741
936976.3644353005171348765
800.049742846519344457
-8895.7426123972694066886
23040.8524069765704963308
336481.1603692528603729876
378649.4185399272732526527
-10544.9656103354915681911
53718.9938177975872477527
-25229.6198006124821929722
15387.1839807538938977294
-70964.9850103617067596105
9.3840494624656214241
24038430.96684856230138706
-3013662.4151196369850486934
-201.3061540908039932589
-1538.6739807611951301207
-5.6191451942422303929
-383.7921403067354350199
6859.0266526803093139166
-544157.4090466279058547576
0.5209107539269847184
-127.8666324936830346752
3831.4679293491412506732
-130349.5149281764137247267
-57238.3722467267318588076
4811.8566533756658134569
1339.0363531615524717677
-33907583.4648414180802540843
1003245.6832190641743985906
-10840.2693777867948236091
61485.6746580190652956975
278854346.4479073562128829805
-438.0754652304676393584
640793.459171935070787981
-3578.0076730887809023325
-1110349.2170089478521030753
-1656457.3631025991090939233
8587.6473186116153651756
-3205.8324583310892293568
223413.2170616239089106697
2379.6129729124326440612
-376.4772366210637083575
-1274.1037002812404986781
3663.782750569200840703
-64089.0850002918708968873
-5721.4209208655819870096
2057.3961821547871457191
50907606.5337233892759565454
810.301986393073753201
130787.6281059496758145612
-11865.4082604328477616477
-2422.4127753056337081914
-11189354.6593492617870325412
-33643.3740618287820524172
-1264553.5525672056444847221
28395402.1215534238423169447
15104.82960034624142943
-2287.7695613276206980026
18902.9584037717509486939
1315.9448985981980532521
-20064521.544348705274127313
5525394.0379106159099135174
9850398.2706809217625256382
1547.2009941826903737936
13128.6925119498854784778
-67292.7775018553374439843
93256.6208938691259959655
-59.5011573429617293645
13.211182626451161305
-1627.8728424038650395048
110899.3025305778402064328
18220.9985031836855864119
257.5143229517866675173
10435.563901503798693748
-124600.9375444905938618204
-28655818.395918968187049049
-38817.8061334052721854554
-210653.862334471439052502
-728776.7389913032121384131
-33996.5408946046870994339
-96188.8533473033934217336
13651.1558657770587009441
91661.8038216957713317366
-1108990.5825454313451837824
-107369.5363696451324500238
38.7836176003353638457
59824.6469414420847153437
22539.9480052462998605876
44630.4407329894428888301
-31576.6269095593559885134
18666198.3160725708020987284
90225788.0289833516368061361
-3920.1816696998862294837
-87472.8740787394063718885
146.218008489509222614
-38133.3099609145689517908
-696.3499082452744218902
3016.1263159598961727914
-381151.0082997857486021791
-1840.4411360065910726755
-5130.613924290242813757
281.5244618100044041922
181853.8111586382406508546
990.4582162961702123749
4942.1315455036937505576
-9291.4533358448216223499
3917777.6166112009129276972
59.8273454118759277728
-26867.0533281068447130982
-159826828.9630376920012307989
-1978187.9694197861983273893
702530.5828382681128730868
-333747.5517382406905523523
-990464.8107009066396824693
10748.2053549781237649091
-7005.1832612002216733688
-74325.5475204521722501307
-25661.7364274927528056494
660622.9003447922443563129
-840738.6601760965413232818
1449794982.2968794741177550972
-237890.5639469191171827345
-511059.6519597705854738019
7702.8090734303900791158
11800332.2192251947500347161
-571379.9934962297980538937
57100319.2949252424745416672
-62.3232483500410667687
953.6578615699993386449
-1441.7567976904636856253
-0.0252653612971505341
7137779.6607716469028546171
-68.695218091661879441
-87836.5451504162016061401
-4.4479287364670102587
1138425.1441228473746708231
-20040.8113799172777461577
-11421.7302306624412328129
238925.7260426806671598324
-7446.0283229740156017896
9388.235134468835981799
-263.7094966993992698215
-66747.0719162683220166006
-94956.7493992628775693059
-42067.5489796188525632063
-8393.0814798217997152905
6167762.5626625872103837996
-293084500.5363248258478218575
458930.9804026872863766932
179321.5418337425324126064
-1220.805880876135195142
-59807072.5378804476584415795
21521.8479936223694551061
-25818970.8532626837096896564
-327418.6908806351177773463
432789.1571582059404087576
-3348.7790941282633317584
-24398.1376595079004188679
1477.8287008897487803133
1265.4685422431991185036
1733231.9010589638686124676
-24231.4443651631177664373
4741.1322090142925142028
853.3050494587379140886
536422.8036699164121425099
-168307.7943199850595990445
2207503.7112625344537043552
-589575.9827363212760553281
76909.9857843671492087394
2500601.7963784952612713906
27446051.2605415964284963112
-2205.0136369379408166083
-2148453.4853628734149113717
-13892.338574804906166967
-488.5080518040085774219
1743.5925261783596185488
448530.2657773465440297977
-876721.2566558269035031117
616720.7691094373723419302
15.3450585167572943033
6237.7015233393049173161
-58801.1167261941342504619
121854.1448068260364120904
-375.1124079184125601142
113029.6627600802611897593
-41.2827864937882649692
2986.5161883271147401895
-334562.3412454615759764942
-3207.9513698960590072423
-130357.7381020248772450846
-288633.3264359707315703989
1859.1154522231549343131
164789.2566160472621866426
284271.5960962697712487771
9663.4014472717706623049
59574.8886916105760784378
-1478010.9524557772268077904
-15001.4815769239115594445
-25201.4050104899670547519
2967888.8513911411624614975
196893.4734437501501706838
3458.2850033825931970229
4869.6663642721522588824
-944.9867018277136455852
30.6575369399001511852
-4.2965022482703842671
-103069569.8751864354501995371
-5521.2482408657591972104
1608.2492102240916274634
-130954.3816662743237630416
1919315474.3097303850767084665
-0.0562767551456997506
-70.1773861876924935631
217889.7903832787166994582
-25811.7181539654997957588
-85281.5408137419733515547
4486.8099259557138272078
518713.467544137758958369
20998.8982731037310305026
-1.2374598641573059997
63624.7305025169334992415
-35774.2484646021896231102
2101.7534769194642291508
11733.0621999918697353889
8633602.389936964306854217
265.037382321492453594
-2316.210170946986646149
-947.8725618009958066848
1.8139024182678573911
1854009.1916279375831977719
-7.849052375420125968
-1732.1603551545201968039
-917754.5530605782607940969
81.2398588703002742432
-17677.1641691586576341731
1925.9388419040667024036
-60.1172608927720784394
3430946.2915632346741881139
-164.4149364143386801835
611863551.4973327142830183284
4081.6907285825886127668
-29714.7657863265339123151
57267.8969645125476495535
9.8062313316474250238
-1448.1596658477588267253
3347.1190285745064509873
5109.3784290119605531249
-806114.2213023084265997168
23400.2285061833053068867
297211.086723815821309949
23230.8415189343565516738
-3510.9140145828268167501
-143238.5264573821670953381
-327689.3095638423633366848
-19842.8812136929402301313
195834.2304013963092315127
-28442621.0725099978704492385
912516.3206426443470082969
1251.7232609472716184494
-1506153757.7655437019649186701
-12207.0035291045729551797
598.1444125940915108345
-393653.2340809659595881083
292.6701966472303612384
157670.9130870018851777022
686.9661607350287691713
5089.9462428229784308589
25909886.5362715647515906396
46668.2786809439895347882
37000.1580568826894284716
-334414.0154919635294493405
-61423.730740835398869294
1231.6589111262234489799
4.0269167128519307236
2635.1036714310115326579
39717.0857803584655262224
33619.257290322673933216
-4405207.5278187446931999286
-64926.6953048309426454112
1443.3110573527349316201
-80.8591243475015452354
55472.8699908007184731005
236.9455047001446825288
-30.5287184644944950766
-115.604402421237437041
-32782.6364920906116019855
-2567930.701076290675306207
-1183524.6218367185432814821
349905.2956523183572271233
-267380.6920366267980038439
-2273860.9743375295955493615
26924.4521526760313567789
34.8433561639288187416
-43715.1956816925410036861
62.8733203682551696494
25152.7533720161716864911
-210.0476881847142538486
1367.5607074353574524288
-2201.9222193443132943597
558320.2024738413648636937
160.1000632101228748208
365177.308763491230461396
-632.1204234280868333396
-76318862.6879199867372816871
-252.6827719200775191598
-120322.6381849748606636632
684354.998591861380125734
-5576.6129492834268967305
23410.8461473024461919086
-228889.4078634156206747123
-2052329.3092233684023019652
-34949.0116743355019735791
2454.6780104029672002667
5405.4721161907882170237
546.0171311435804063769
-447.9705567115010597384
-21604.3775856323518625872
707.5386859533371512304
-146422.1782903817508427142
4 open "ratvalva.txt" for output as #2
5 dim Used(97),V(97)
10 for Trial=1 to 500
20 erase Used():dim Used(97)
30 erase V():dim V(97)
36 for I=1 to 97
37 V(I)=49//I
38 next
40 Usedct=0
50 while Usedct<96
60 repeat
70 R=int(rnd*97+1)
80 until Used(R)=0
90 N1=V(R):Used(R)=1:V(R)=0
100 repeat
110 R=int(rnd*97+1)
120 until Used(R)=0
130 N2=V(R):V(R)=N1*N2-N1-N2+1
140 inc Usedct
150 wend
155 if Trial<4 then
160 :print V(R),V(R)/1
161 :print #2,V(R),V(R)/1
162 :else
163 :print #2,V(R)/1
300 next
310 close #2
|
|
Posted by Charlie
on 2016-03-20 10:14:35 |
a sampling of 500 at random
