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IMAS 2023–2024 Junior Division — First Round Question 8

IMAS · IMAS 2023–2024 Junior Division — First Round

Question 8

Eight different digits are written in each cell of a table with 2 rows and 4 columns. Each cell is written exactly one digit. The sum of the digits in any of the two rows is divisible by 7, while the sum of the digits in any of the four columns is an even number. If $a$ and $b$ are the only two digits that are not written in the table, what is the number of possible values for $|a-b|$?
  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. $5$