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Friday, 6 june 2008 |
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Max number of numbers... |
Proposed by
mdaniel |
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| (27 comments) | 10.739 times displayed |
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Care este numarul maxim de cifre ce pot fi sterse din numarul de 1000 de cifre 200820082008...2008 astfel incat suma cifrelor ramase sa fie 2008? |
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deci ne intereseaza care este numarul minim de cifre care ramane astfel incat suma lor sa dea 2008
presupunand ca ne vor ramane doar cifre de 2 si 8, trebuie satisfacuta relatia:
2x + 8y = 2008, unde x si y reprezinta numarul cifrelor de 2 si respectiv 8
deci 2x = 2008 - 8y = 8(251 - y),
adica x = 4(251 - y), unde observam ca numarul minim acceptat de x este 4, de unde 251 - y = 1, de unde y = 250
deci, vom avea 4 cifre de 2 si 250 cifre de 8, in total 4+250 = 254 cifre
daca vom da lui y valoarea minima adica 1, vom obtine x = 4(251-1) = 4*250 = 1000, deci vom avea 1000 cifre de 2 si o cifra de 8, in total 1001 cifre
solutie va fi prima varianta gasita, adica raman 254 cifre, deci se sterg 1000-254 = 746 cifre
numai bine.... |
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numbers
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