Question

Ce numar natural se micsoreaza cu 2017 daca ii stergem ultimele 2 cifre

Answer 1

$\overline{ab} = \overline{abcd}-2017$

=> ...

$a \in \{1,2,3,4,5,6,7,8,9\}\\b \in \{0,1,2,3,4,5,6,7,8,9\}$

Daca:

$\overline{ab} < 20 = > se \; obtine\; numar\;negativ\\\overline{ab} > 20 = > se\;obtine\;numar\;mai\;mare\;decat\;(2100-2017)=83$

=> Trebuie indeplinita urmatoarea conditie:

$\overline{ab}=20 = > a=2\;\;si\;\;b=0$

$= > 20=\overline{20cd}-2017=2000+\overline{cd}-2000-17\\= > 20=\overline{cd}-17\\= > \overline{cd}=20+17=37 \\= > c=3\;\;si\;\;d=7$

Raspuns:

$\overline{abcd}=2037$ => Numarul cautat este 2037