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Topic: Brainteaser n
Replies: 15   Last Post: Aug 6, 2003 7:10 AM

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 Daniel Joseph Min Posts: 57 Registered: 12/13/04
Brainteaser n
Posted: Jan 13, 2003 12:20 AM

Here is a test of your powers of inspection and inductive logic. To solve
it requires no more than high school math. It is much easier than it looks.

X, an integer with just over 6100 decimal digits, is resolved into prime
factors as follows:
3^54 * 7^20 * 11^60 * 13^19 * 17^6 * 19^6 * 23^5 * 29^3 * 31^7 * 37^38 *
41^22 * 43^5 * 47^2 * 53^8 * 59 * 61 * 67^3 * 71^3 * 73^13 * 79^8 * 83^2 *
89^2 * 97 * 101^27 * 103^3 * 107^2 * 109 * 127^2 * 137^13 * 139^2 * 151 *
157 * 163 * 173^2 * 191 * 197 * 199 * 211^3 * 239^15 * 241^3 * 251^2 *
271^22 * 277 * 281^3 * 317 * 331 * 353^3 * 397 * 449^3 * 521^2 * 547 *
613^2 * 617 * 641^3 * 643 * 733 * 757^4 * 859^4 * 1031 * 1231^2 * 1289 *
1321^2 * 1409^3 * 1933^5 * 2161^3 * 2531^2 * 2689^2 * 2791^3 * 3169 *
3191^3 * 3541^5 * 4003 * 4013^3 * 4093^5 * 4201 * 4637 * 4649^15 * 5051^2 *
5171 * 5237 * 6163 * 6299 * 6397 * 7253 * 7841 * 8779^5 * 9091^11 * 9397 *
9901^9 * 10271 * 10837 * 14197 * 16763^3 * 17837 * 19841 * 21319 * 21401^4
* 21649^10 * 23311 * 25601^4 * 27961^5 * 29611 * 34849 * 42043 * 43037^3 *
45613 * 52579^6 * 59281 * 60101 * 62003^3 * 62921^2 * 63841 * 69857^3 *
72559 * 98641 * 123551^3 * 153469 * 206209 * 210631^2 * 216451 * 226549 *
238681^2 * 307627 * 329401 * 333667^12 * 459691^2 * 493121 * 497867 *
513239^10 * 538987^2 * 909091^7 * 974293 * 976193 * 999809 * 1192679 *
1527791^2 * 1580801 * 1659431^2 * 1676321^2 * 2028119^3 * 2071723^6 *
2462401 * 2906161^7 * 3762091 * 4147571 * 4188901 * 4262077 * 5070721 *
5882353^6 * 6187457 * 6943319^3 * 7019801 * 7034077 * 9885089 * 10749631 *
10838689^5 * 12004721 * 28559389 * 29920507 * 35121409^2 * 39526741 *
45121231 * 52986961^2 * 57009401 * 70541929^2 * 83251631^2 * 99990001^4 *
103733951 * 121499449^3 * 215257037 * 247629013^3 * 262533041 * 265371653^8
* 505885997^2 * 599144041 * 1052788969^2 * 1056689261^2 * 1058313049^4 *
1360682471 * 1491383821 * 2182600451 * 2386760191 * 5363222357^6 *
5964848081^2 * 12171337159 * 14175966169^2 * 20163494891 * 21993833369^3 *
30703738801 * 43442141653 * 66554101249 * 77843839397^3 * 104984505733 *
162503518711 * 182521213001^4 * 183411838171 * 291078844423 * 388847808493
* 625437743071 * 985695684401 * 999999000001^3 * 2559647034361 *
3367147378267 * 8119594779271 * 14103673319201 * 18371524594609 *
75118313082913 * 78875943472201^2 * 106007173861643 * 203864078068831 *
422650073734453 * 440334654777631^4 * 549797184491917^2 * 676421558270641 *
834427406578561 * 1680588011350901 * 1921436048294281 * 1963506722254397^2
* 2324557465671829 * 3199044596370769 * 4855067598095567 *
9999999900000001^2 * 13168164561429877^2 * 30557051518647307 *
102598800232111471^3 * 265212793249617641 * 296557347313446299 *
316877365766624209 * 511399538427507881 * 646826950155548399 *
722817036322379041 * 909090909090909091^2 * 1111111111111111111^5 *
1325815267337711173^2 * 1344628210313298373^3 * 1369778187490592461 *
1855193842151350117 * 2140992015395526641^2 * 2670502781396266997 *
4185502830133110721^2 * 4458192223320340849 * 7061709990156159479 *
49172195536083790769 * 57336415063790604359^3 * 79863595778924342083 *
127522001020150503761 * 377526955309799110357 * 712767480971213008079 *
1900381976777332243781^2 * 2212394296770203368013^3 *
3404193829806058997303 * 5295275348767234696493 * 11111111111111111111111^4
* 318727841165674579776721 * 900900900900990990990991^2 *
1300635692678058358830121^2 * 3931123022305129377976519 *
5078554966026315671444089 * 7306116556571817748755241 *
8845981170865629119271997 * 19721061166646717498359681 *
47198858799491425660200071^2 * 57802050308786191965409441 *
110742186470530054291318013 * 130654897808007778425046117 *
154083204930662557781201849 * 297262705009139006771611927 *
1289981231950849543985493631 * 1595352086329224644348978893 *
4181003300071669867932658901 * 4531530181816613234555190841 *
9512538508624154373682136329 * 59779577156334533866654838281 *
90077814396055017938257237117 * 201763709900322803748657942361^2 *
241573142393627673576957439049 * 909090909090909090909090909091 *
129063282232848961951985354966759 * 965194617121640791456070347951751 *
1976730144598190963568023014679333^2 * 15763985553739191709164170940063151
* 846035731396919233767211537899097169 *
5538396997364024056286510640780600481 *
10288079467222538791302311556310051849 *
16205834846012967584927082656402106953 *
316362908763458525001406154038726382279^2 *
403513310222809053284932818475878953159 *
5076141624365532994918781726395939035533 *
18998088572819375252842078421374368604969 *
28213380943176667001263153660999177245677 *
45994811347886846310221728895223034301839 *
346895716385857804544741137394505425384477 *
632527440202150745090622412245443923049201 *
3660574762725521461527140564875080461079917 *
4222100119405530170179331190291488789678081 *
49207341634646326934001739482502131487446637 *
136614668576002329371496447555915740910181043 *
4340876285657460212144534289928559826755746751 *
310170251658029759045157793237339498342763245483 *
362853724342990469324766235474268869786311886053883 *
9090909090909090909090909090909090909090909090909091 *
109399846855370537540339266842070119107662296580348039 *
246829743984355435962408390910378218537282105150086881669547 *
900900900900900900900900900900990990990990990990990990990991 *
153211620887015423991278431667808361439217294295901387715486473457925534859
044796980526236853

Provide a short (37 ASCII characters suffice), simple (the only operators
being add and multiply; no factorials) expression that yields X.

Hints (1) You do not need to numerically compute X. It will not help.
(2) Sometimes, what is not there is as significant as what is there.
(3) The expression is elegant in its economy.

Have fun!

--
Bourbaki

Date Subject Author
1/13/03 Daniel Joseph Min
1/13/03 Virgil
1/13/03 Daniel Joseph Min
1/13/03 William Hart
1/13/03 William Hart
1/13/03 Daniel Joseph Min
1/13/03 William Hart
1/13/03 William Hart
1/14/03 Jeroen Boschma
1/14/03 William Hart
1/13/03 The Last Danish Pastry
1/13/03 Daniel Joseph Min
1/13/03 David C. Ullrich
1/14/03 The Last Danish Pastry
1/14/03 The Last Danish Pastry
8/6/03 anonymous