Difference between revisions of "2016 JBMO Problems/Problem 4"
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== Problem == | == Problem == | ||
| − | A <math>5 \times 5</math> table is called regular if each of its cells contains one of four pairwise distinct real numbers,such that each of them occurs exactly | + | A <math>5 \times 5</math> table is called regular if each of its cells contains one of four pairwise distinct real numbers, such that each of them occurs exactly once in every <math>2 \times 2</math> subtable.The sum of all numbers of a regular table is called the total sum of the table. With any four numbers, one constructs all possible regular tables, computes their total sums, and counts the distinct outcomes. Determine the maximum possible count. |
== Solution == | == Solution == | ||
Revision as of 00:48, 12 January 2023
Problem
A 
table is called regular if each of its cells contains one of four pairwise distinct real numbers, such that each of them occurs exactly once in every 
subtable.The sum of all numbers of a regular table is called the total sum of the table. With any four numbers, one constructs all possible regular tables, computes their total sums, and counts the distinct outcomes. Determine the maximum possible count.
Solution
See also
| 2016 JBMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Last Problem | |
| 1 • 2 • 3 • 4 | ||
| All JBMO Problems and Solutions | ||
