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Found problems: 1

2011 Bosnia and Herzegovina Junior BMO TST, 4
Tags: number puzzle , combinatorics
Let us consider mathematical crossword which we fill with numbers $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ such that: 1) All digits occur exactly twice 2) $10$ horizontally divides $4$ vertically 3) $4 \cdot$ ($4$ horizontally - $4$ vertically +$5$) equals $1$ vertically 4) $36$ divides $1$ horizontally and $5$ vertically 5) $9$ vertically divides $5$ vertically In how many ways we can solve this mathematical crossword? [img]https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOC85LzgyNjUzYmNkNTVmNDE1YTg4OWVkNzAzYzE1M2JkZWE0MThiYWY1LnBuZw==&rn=Y3Jvc3N3b3JkLnBuZw==[/img]