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IMO 1968 — Shortlist problems Question 24

IMO Shortlist · IMO 1968 — Shortlist problems

Question 24

(MON 1) Find the number of all $n$-digit numbers for which some fixed digit stands only in the $i$th $(1\lt i\lt n)$ place and the last $j$ digits are distinct.

Source footnote 3. The problem is unclear. Presumably $n,i,j$ and the $i$th digit are fixed.