P:1793: Difference between revisions

Revision as of 14:09, 17 August 2025

P:1793 (Ioana Roman)]]

Determinați cel mai mic număr de forma Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abcd}} pentru care are loc egalitatea Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1+\overline{abcd}= 88 \times \overline{cd}} .

Soluție

Egalitatea din enunț se scrie în mod echivalent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1+\overline{ab} \times 100 + \overline{cd}= 88 \times \overline{cd}} , ceea ce conduce la Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{ab01}= 87 \times \overline{cd}.} Cum doar produsul Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7 \times 3} are ultima cifră egală cu Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} , deducem că Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d= 3} .

Avem produsele

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 13 = 1131} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 23 = 2001} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 33 = 2871} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 43 = 3741} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 53 = 4611} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 63 = 5481} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 73 = 6351} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 83 = 7221} Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 93 = 8091}

de unde deducem că doar produsul Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 87 \times 23 = 2001} este cel care corespunde.

În concluzie, unicul număr de forma Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abcd}} pentru care are loc egalitatea Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1+\overline{abcd}= 88 \times \overline{cd}} este Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abcd} = 2023.}

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 '''Soluție'''
-Egalitatea din enunț se scrie în mod echivalent  <math>1+\overline{ab} \times 100 + \overline{cd}= 88 \times \overline{cd}</math>, ceea ce conduce la <math display="block">\overline{ab01}= 87 \times \overline{cd}</math>.
-Cum doar produsul <math>7 \times 3</math> are ultima cifră egală cu <math>1</math>, deducem că <math>d= 3</math>.
+Egalitatea din enunț se scrie în mod echivalent  <math>1+\overline{ab} \times 100 + \overline{cd}= 88 \times \overline{cd}</math>, ceea ce conduce la <math display="block">\overline{ab01}= 87 \times \overline{cd}.</math>Cum doar produsul <math>7 \times 3</math> are ultima cifră egală cu <math>1</math>, deducem că <math>d= 3</math>.
 Avem produsele
-<math>87 \times 13 = 1131</math>
+<math display="block">87 \times 13 = 1131</math><math display="block">87 \times 23 = 2001</math><math display="block">87 \times 33 = 2871</math><math display="block">87 \times 43 = 3741</math><math display="block">87 \times 53 = 4611</math><math display="block">87 \times 63 = 5481</math><math display="block">87 \times 73 = 6351</math><math display="block">87 \times 83 = 7221</math><math display="block">87 \times 93 = 8091</math>
-<math>87 \times 23 = 2001</math>
-<math>87 \times 33 = 2871</math>
-<math>87 \times 43 = 3741</math>
-<math>87 \times 53 = 4611</math>
-<math>87 \times 63 = 5481</math>
-<math>87 \times 73 = 6351</math>
-<math>87 \times 83 = 7221</math>
-<math>87 \times 93 = 8091</math>
 de unde deducem că doar produsul  <math>87 \times 23 = 2001</math> este cel care corespunde.
-În concluzie, unicul număr de forma <math>\overline{abcd}</math> pentru care are loc egalitatea <math>1+\overline{abcd}= 88 \times \overline{cd}</math> este <math display="block">2023</math>.
+În concluzie, unicul număr de forma <math>\overline{abcd}</math> pentru care are loc egalitatea <math>1+\overline{abcd}= 88 \times \overline{cd}</math> este <math display="block">\overline{abcd} = 2023.</math>