Let $n$ and $r$ be two given positive integers. We wish to construct $r$ subsets $A_1, A_2, \ldots, A_r$ of $\{0,1, \ldots, n-1\}$, each of cardinality $k$, such that for each integer $x$ with $0 \leq x \leq n-1$ there exist ...

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Let $n$ and $r$ be two given positive integers. We wish to construct $r$ subsets $A_1, A_2, \ldots, A_r$ of $\{0,1, \ldots, n-1\}$, each of cardinality $k$, such that for each integer $x$ with $0 \leq x \leq n-1$ there exist elements $x_i \in A_i(i=1, \ldots, n)$ with $x=x_1+x_2+\cdots+x_r$. Find the minimum value of $k$.

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Sep 23 in Mathematics by ♦MathsGee Platinum (138,598 points) | 29 views

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935

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Let \(n\) and \(r\) be two given positive integers. We wish to construct \(r\) subsets \(A_1, A_2, \ldots, A_r\) of \(\{0,1, \ldots, n-1\}\), each of cardinality \(k\), such that for each integer \(x\) with \(0 \leq x \leq n-1\) there exist ...

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Let \(n\) and \(r\) be two given positive integers. We wish to construct \(r\) subsets \(A_1, A_2, \ldots, A_r\) of \(\{0,1, \ldots, n-1\}\), each of cardinality \(k\), such that for each integer \(x\) with \(0 \leq x \leq n-1\) there exist ...

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