Dati i numeri 1, 2, 3, …, 100, trovate un metodo per selezionare un insieme di 51 numeri distinti tale che nell’insieme ci sia sempre una coppia di numeri primi tra loro.
La risposta... Non cliccate qui se non ci avete pensato! Poi è troppo tardi!
Qualsiasi insieme che non comprenda il valore 1 soddisfa la condizione.
Infatti, se dividiamo i numeri in sottoinsiemi {1, 2}, {3, 4}, {5, 6}, … {99, 100}, essendo questi cinquanta, quando prenderemo cinquantun numeri dovremo forzatamente prenderne due da uno dei sottoinsiemi, e due numeri consecutivi maggiori o uguali a 2 sono primi tra loro.
I Rudi Mathematici (Rodolfo Clerico / Rudy d’Alembert, Piero Fabbri / Piotr Rezierovic Silverbrahms, Francesca Ortenzio / Alice Riddle) sono autori della omonima e-zine di matematica ricreativa, pubblicata in rete dal 1999.
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