Salutare!
Cerinta:
"Determinati toate numerele de forma ab stiind ca a5b e mai mare decat 754"
Rezolvare:
[tex]\bf \overline{ab}[/tex] = ???
a,b - cifre
cifrele sunt: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
a,b,c,d ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
a ≠ 0 (deoarece un numar nu poate incepe cu cifra zero)
[tex]\bf 754>\overline{a5b} \implies[/tex] a ≥ 7
a ≥ 7 ⇒ a ∈ {7, 8, 9}
Analizam fiecare valoare pe care o poate lua a, astfel avem 3 cazuri:
a = 7 ⇒ b > 4 ⇒ b ∈ {5, 6, 7, 8, 9} ⇒
[tex]\bf \overline{a5b} \in\{755,756,757,758,759\}[/tex] ⇒
[tex]\bf \overline{ab} \in\{75,76,77,78,79\}\implies\text{\it 5 numere}[/tex]
a = 8 ⇒ b ∈ {0,1,2,3,4,5,6,7,8,9} ⇒
[tex]\bf \overline{a5b} \in\{850,851,852,853,854,855,856,857,858,859\}[/tex] ⇒
[tex]\bf \overline{ab} \in\{80,81,82,83,84,85,86,87,88,89\}\implies\text{\it 10 numere}[/tex]
a = 9 ⇒ b ∈ {0,1,2,3,4,5,6,7,8,9} ⇒
[tex]\bf \overline{a5b} \in\{950,951,952,953,954,955,956,957,958,959\}[/tex] ⇒
[tex]\bf \overline{ab} \in\{90,91,92,93,94,95,96,97,98,99\}\implies\text{\it 10 numere}[/tex]
Din cele trei cazuri analizate avem:
5 + 10 + 10 = 25 de numere de forma [tex]\bf \overline{ab}[/tex] care respecta conditiile problemei
[tex]\bf \overline{ab} \in\{{75,76,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99\}[/tex]
==pav38==
