Caccia al tesoro

Cercatori d'oro, in California, poco dopo la scoperta dell'oro in questo Stato, nel 1848.

C'era una volta, ma c'era davvero, non è una favola, un cercatore d'oro che sotterrò un tesoro in oro, argento e gioielli del valore attuale superiore ai 15 milioni di Euro. In tre crittogrammi è indicato il punto esatto in cui si trova. Thomas J. Beale, questo è il suo nome, lasciò i messaggi a un amico nel 1825 e quest'ultimo, non avendo più notizie di Beale, decise di renderli pubblici nel 1885. Da allora centinaia di cacciatori di tesori hanno tentato invano di scoprire il favoloso tesoro.

Pubblichiamo i tre crittogrammi consistenti in tre pagine fitte di numeri. Finora soltanto il secondo è stato decifrato e sappiamo così che il tesoro si trova in Virginia, "nella contea di Bedford, a circa quattro miglia da Buford's, in una fossa, o cripta, sei piedi sotto la superficie del suolo".
In questo caso Beale ha usato una cifratura chiamata book cipher che consiste nel fare riferimento a un testo chiave, e Beale ha scelto la Dichiarazione d'Indipendenza degli Stati Uniti. E' sufficiente assegnare a ogni parola del testo un numero crescente e sostituire a ogni lettera del messaggio che vogliamo crittografare il numero che indica la lettera iniziale della parola corrispondente del testo chiave.

Prendiamo, ad esempio, i versi di Dante:

1Nel 2mezzo 3del 4cammin 5di 6nostra 7vita
8mi 9ritrovai 10per 11una 12selva 13oscura,
14ché 15la 16diritta 17via 18era 19smarrita.

20Ahi 21quanto 22a 23dir 24qual 25era 26è 27cosa 28dura,

La frase: "un nuovo eroe del mare"
diventa: "11, 1, 6, 11, 13, 7, 13, 25, 9, 13, 18, 5, 18, 15, 2, 22, 9, 18"

Con questi pochi versi non abbiamo ancora a disposizione tutte le lettere dell'alfabeto, ma sarà sufficiente per questo ricorrere a un testo chiave più lungo.
Qui di seguito riportiamo i tre crittogrammi e per il secondo anche l'inizio della Dichiarazione d'Indipendenza, cioè il testo chiave, e inoltre il testo del messaggio decifrato, in inglese e nella traduzione italiana.
A questo punto se qualcuno vuol partecipare alla caccia al tesoro ha tutti gli elementi disponibili per tentare.

Chi fosse interessato ad approfondire la storia di Beale e, più in generale, i misteri della crittografia legga Codici & Segreti di Simon Singh, pubblicato da Rizzoli, un libro affascinante, sicuramente uno dei più bei libri di divulgazione matematica degli ultimi anni.

Una rara fotografia del 1850 con cercatori d'oro in California.

Il primo crittogramma

71,194,38,1701,89,76,11,83,1629,48,94,63,132,16,111,95,84,341
975,14,40,64,27,81,139,213,63,90,1120,8,15,3,126,2018,40,74
758,485,604,230,436,664,582,150,251,284,308,231,124,211,486,225
401,370,11,101,305,139,189,17,33,88,208,193,145,1,94,73,416
918,263,28,500,538,356,117,136,219,27,176,130,10,460,25,485,18
436,65,84,200,283,118,320,138,36,416,280,15,71,224,961,44,16,401
39,88,61,304,12,21,24,283,134,92,63,246,486,682,7,219,184,360,780
18,64,463,474,131,160,79,73,440,95,18,64,581,34,69,128,367,460,17
81,12,103,820,62,110,97,103,862,70,60,1317,471,540,208,121,890
346,36,150,59,568,614,13,120,63,219,812,2160,1780,99,35,18,21,136
872,15,28,170,88,4,30,44,112,18,147,436,195,320,37,122,113,6,140
8,120,305,42,58,461,44,106,301,13,408,680,93,86,116,530,82,568,9
102,38,416,89,71,216,728,965,818,2,38,121,195,14,326,148,234,18
55,131,234,361,824,5,81,623,48,961,19,26,33,10,1101,365,92,88,181
275,346,201,206,86,36,219,324,829,840,64,326,19,48,122,85,216,284
919,861,326,985,233,64,68,232,431,960,50,29,81,216,321,603,14,612
81,360,36,51,62,194,78,60,200,314,676,112,4,28,18,61,136,247,819
921,1060,464,895,10,6,66,119,38,41,49,602,423,962,302,294,875,78
14,23,111,109,62,31,501,823,216,280,34,24,150,1000,162,286,19,21
17,340,19,242,31,86,234,140,607,115,33,191,67,104,86,52,88,16,80
121,67,95,122,216,548,96,11,201,77,364,218,65,667,890,236,154,211
10,98,34,119,56,216,119,71,218,1164,1496,1817,51,39,210,36,3,19
540,232,22,141,617,84,290,80,46,207,411,150,29,38,46,172,85,194
39,261,543,897,624,18,212,416,127,931,19,4,63,96,12,101,418,16,140
230,460,538,19,27,88,612,1431,90,716,275,74,83,11,426,89,72,84
1300,1706,814,221,132,40,102,34,868,975,1101,84,16,79,23,16,81,122
324,403,912,227,936,447,55,86,34,43,212,107,96,314,264,1065,323
428,601,203,124,95,216,814,2906,654,820,2,301,112,176,213,71,87,96
202,35,10,2,41,17,84,221,736,820,214,11,60,760


Il secondo crittogramma

115,73,24,807,37,52,49,17,31,62,647,22,7,15,140,47,29,107,79,84
56,239,10,26,811,5,196,308,85,52,160,136,59,211,36,9,46,316,554
122,106,95,53,58,2,42,7,35,122,53,31,82,77,250,196,56,96,118,71
140,287,28,353,37,1005,65,147,807,24,3,8,12,47,43,59,807,45,316
101,41,78,154,1005,122,138,191,16,77,49,102,57,72,34,73,85,35,371
59,196,81,92,191,106,273,60,394,620,270,220,106,388,287,63,3,6
191,122,43,234,400,106,290,314,47,48,81,96,26,115,92,158,191,110
77,85,197,46,10,113,140,353,48,120,106,2,607,61,420,811,29,125,14
20,37,105,28,248,16,159,7,35,19,301,125,110,486,287,98,117,511,62
51,220,37,113,140,807,138,540,8,44,287,388,117,18,79,344,34,20,59
511,548,107,603,220,7,66,154,41,20,50,6,575,122,154,248,110,61,52,33
30,5,38,8,14,84,57,540,217,115,71,29,84,63,43,131,29,138,47,73,239
540,52,53,79,118,51,44,63,196,12,239,112,3,49,79,353,105,56,371,557
211,505,125,360,133,143,101,15,284,540,252,14,205,140,344,26,811,138
115,48,73,34,205,316,607,63,220,7,52,150,44,52,16,40,37,158,807,37
121,12,95,10,15,35,12,131,62,115,102,807,49,53,135,138,30,31,62,67,41
85,63,10,106,807,138,8,113,20,32,33,37,353,287,140,47,85,50,37,49,47
64,6,7,71,33,4,43,47,63,1,27,600,208,230,15,191,246,85,94,511,2,270
20,39,7,33,44,22,40,7,10,3,811,106,44,486,230,353,211,200,31,10,38
140,297,61,603,320,302,666,287,2,44,33,32,511,548,10,6,250,557,246
53,37,52,83,47,320,38,33,807,7,44,30,31,250,10,15,35,106,160,113,31
102,406,230,540,320,29,66,33,101,807,138,301,316,353,320,220,37,52
28,540,320,33,8,48,107,50,811,7,2,113,73,16,125,11,110,67,102,807,33
59,81,158,38,43,581,138,19,85,400,38,43,77,14,27,8,47,138,63,140,44
35,22,177,106,250,314,217,2,10,7,1005,4,20,25,44,48,7,26,46,110,230
807,191,34,112,147,44,110,121,125,96,41,51,50,140,56,47,152,540
63,807,28,42,250,138,582,98,643,32,107,140,112,26,85,138,540,53,20
125,371,38,36,10,52,118,136,102,420,150,112,71,14,20,7,24,18,12,807
37,67,110,62,33,21,95,220,511,102,811,30,83,84,305,620,15,2,108,220
106,353,105,106,60,275,72,8,50,205,185,112,125,540,65,106,807,188,96,110
16,73,32,807,150,409,400,50,154,285,96,106,316,270,205,101,811,400,8
44,37,52,40,241,34,205,38,16,46,47,85,24,44,15,64,73,138,807,85,78,110
33,420,505,53,37,38,22,31,10,110,106,101,140,15,38,3,5,44,7,98,287
135,150,96,33,84,125,807,191,96,511,118,440,370,643,466,106,41,107
603,220,275,30,150,105,49,53,287,250,208,134,7,53,12,47,85,63,138,110
21,112,140,485,486,505,14,73,84,575,1005,150,200,16,42,5,4,25,42
8,16,811,125,160,32,205,603,807,81,96,405,41,600,136,14,20,28,26
353,302,246,8,131,160,140,84,440,42,16,811,40,67,101,102,194,138
205,51,63,241,540,122,8,10,63,140,47,48,140,288


Il terzo crittogramma

317,8,92,73,112,89,67,318,28,96,107,41,631,78,146,397,118,98
114,246,348,116,74,88,12,65,32,14,81,19,76,121,216,85,33,66,15
108,68,77,43,24,122,96,117,36,211,301,15,44,11,46,89,18,136,68
317,28,90,82,304,71,43,221,198,176,310,319,81,99,264,380,56,37
319,2,44,53,28,44,75,98,102,37,85,107,117,64,88,136,48,154,99,175
89,315,326,78,96,214,218,311,43,89,51,90,75,128,96,33,28,103,84
65,26,41,246,84,270,98,116,32,59,74,66,69,240,15,8,121,20,77,80
31,11,106,81,191,224,328,18,75,52,82,117,201,39,23,217,27,21,84
35,54,109,128,49,77,88,1,81,217,64,55,83,116,251,269,311,96,54,32
120,18,132,102,219,211,84,150,219,275,312,64,10,106,87,75,47,21
29,37,81,44,18,126,115,132,160,181,203,76,81,299,314,337,351,96,11
28,97,318,238,106,24,93,3,19,17,26,60,73,88,14,126,138,234,286
297,321,365,264,19,22,84,56,107,98,123,111,214,136,7,33,45,40,13
28,46,42,107,196,227,344,198,203,247,116,19,8,212,230,31,6,328
65,48,52,59,41,122,33,117,11,18,25,71,36,45,83,76,89,92,31,65,70
83,96,27,33,44,50,61,24,112,136,149,176,180,194,143,171,205,296
87,12,44,51,89,98,34,41,208,173,66,9,35,16,95,8,113,175,90,56
203,19,177,183,206,157,200,218,260,291,305,618,951,320,18,124,78
65,19,32,124,48,53,57,84,96,207,244,66,82,119,71,11,86,77,213,54
82,316,245,303,86,97,106,212,18,37,15,81,89,16,7,81,39,96,14,43
216,118,29,55,109,136,172,213,64,8,227,304,611,221,364,819,375
128,296,1,18,53,76,10,15,23,19,71,84,120,134,66,73,89,96,230,48
77,26,101,127,936,218,439,178,171,61,226,313,215,102,18,167,262
114,218,66,59,48,27,19,13,82,48,162,119,34,127,139,34,128,129,74
63,120,11,54,61,73,92,180,66,75,101,124,265,89,96,126,274,896,917
434,461,235,890,312,413,328,381,96,105,217,66,118,22,77,64,42,12
7,55,24,83,67,97,109,121,135,181,203,219,228,256,21,34,77,319,374
382,675,684,717,864,203,4,18,92,16,63,82,22,46,55,69,74,112,134
186,175,119,213,416,312,343,264,119,186,218,343,417,845,951,124
209,49,617,856,924,936,72,19,28,11,35,42,40,66,85,94,112,65,82
115,119,233,244,186,172,112,85,6,56,38,44,85,72,32,47,63,96,124
217,314,319,221,644,817,821,934,922,416,975,10,22,18,46,137,181
101,39,86,103,116,138,164,212,218,296,815,380,412,460,495,675,820
952

Dichiarazione d'Indipendenza, testo chiave del secondo messaggio

When1, in2 the3 course4 of5 human6 events7 it8 becomes9 necessary10 for one people to dissolve the political bands which have (20) connected them with another. and to assume among the powers (30) of the earth, the separate and equal station to which (40) the laws of nature and of nature's God entitle them, (50) a decent respect to the opinions of mankind requires that (60) they should declare the causes which impel them to the (70) separation.
We hold these truths to be self-evident, that (80) all men are created equal: that they are endowed by (90) their Creator with certain inalienable rights: that among these are (100) life, liberty, and the pursuit of happiness; that to secure (110) their rights, governments are instituted among men, deriving their just (120) powers from the consent of the governed; that when any (130) form of government becomes destructive of these ends, it is (140) the right of the people to alter or to abolish (150) it, and to institute a new government, laying its foundation (160) on such principles and organizing its powers in such form, (170) as to them shall seem most likely to effect their (180) safety and happiness. Prudence, indeed, will dictate that governments long (190) established, should not be changed for light and transient causes; (200) and accordingly all experience hath shown that mankind are now (210) disposed to suffer, while evils are sufferable, than to right (220) themselves by abolishing the forms to which they are accustomed. (230) But, when a long train of abuses and usurpations, pursuing (240) invariably the same object, evinces a design to reduce them under(250) absolute despotism, it is their right, it is their duty, (260) to throw off such government, and to provide new guards (270) for their future security. Such has been the patient sufferance (280) of these colonies, and such is now the necessity which (290) constrains them to alter their former systems of government. The (300) history of the present King of
Great Britain is a (310) history of repeated injuries and usurpations, all having in direct (320) object the establishment of an absolute tyranny over these States. (330) To prove this, let facts be submitted to a candid (340) world.
He has refused his assent to laws the most (350) wholesome and necessary for the public good. He has forbidden (360) his governors to pass laws of immediate and pressing importance, (370) unless suspended in their operation till his assent should be(380) obtained; and when so suspended he has utterly neglected to (390) attend to them.
He has refused to pass other laws (400) for the accommodation of large districts of people, unless those (410) people would relinquish their right of representation in the legislature, (420) a right inestimable to them and formidable to tyrants only. (430)
He has called together legislative bodies at places unusual, uncomfortable (440) and distant from the depository of their public records, for (450) the sole purpose of fatiguing them into compliance with his (460) measures.

Il testo del secondo messaggio

I have deposited, in the county of Bedford, about four miles from Buford's, in an excavation or vault, six feet below the surface of the ground, the following articles, belonging jointly to the parties whose names are given in number "3," herewith:
The first deposit consisted of one thousand and fourteen pounds of gold, and three thousand eight hundred and twelve pounds of silver, deposited November, 1819. The second was made December, 1821, and consisted of nineteen hundred and seven pounds of gold, and twelve hundred and eighty-eight pounds of silver; also jewels, obtained in St. Louis in exchange for silver to save transportation, and valued at $13,000.
The above is securely packed in iron pots, with iron covers. The vault is roughly lined with stone, and the vessels rest on solid stone, and are covered with others. Paper number "1" describes the exact locality of the vault, so that no difficulty will be had in finding it.

Incisione delle miniere d'oro del Colorado, nel 1859.

La traduzione

Ho depositato, nella contea di Bedford, a circa quattro miglia da Buford's, in una fossa, o cripta, sei piedi sotto la superficie del suolo, i seguenti articoli che appartengono congiuntamente alle persone i cui nomi vengono forniti nell'allegato numero 3:
Il primo deposito consiste in mille e quattordici libbre di oro e tremilaottocentododici libbre di argento, depositate nel Novembre del 1819. Il secondo è stato effettuato nel Dicembre del 1821 e consiste in millenovecentosette libbre d'oro e milleduecentootto libbre d'argento, oltre a gioielli ottenuti a St. Louis in cambio dell'argento per risparmiare sul trasporto e valutati tredicimila dollari. Quanto sopra è conservato in contenitori di ferro con coperchi di ferro. La cripta è rozzamente delimitata da pietre e i forzieri poggiano su solide pietre, coperti a loro volta da altre pietre. Il foglio numero 1 descrive l'esatta località della cripta, cosicchè non vi saranno difficoltà nel trovarla.

Cercatori d'oro sulla Pista Chilkoot, una delle più importanti vie della Corsa all'oro, 1897.