ways to fill x 3x8 grid by 9 numbers having 6 already in fixed places

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Source: Mathematics Regional Olympiad of Mexico Center Zone 2016 P1

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#1 h Nov 12, 2021, 7:33 PM

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The grid shown below is completed by choosing nine of the following numbers without repeating: $4, 5, 6, 7, 8, 12, 13, 16, 18, 19$ . If the sum of the five rows are equal to each other and the sum of the three columns are equal to each other, in how many different ways is it possible to fill the grid?

$\begin {array} {| c | c | c |} \hline 10 & & \\ \hline & & 9 \\ \hline & 3 & \\ \hline 11 & & 17 \\ \hline & 20 & \\ \hline \end {array}$

Note: The sum of the rows and the sum of the columns are not necessarily equal.

This post has been edited 1 time. Last edited by parmenides51, Nov 12, 2021, 7:33 PM

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