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IMO LongList 1985 CAN4 - Superchess game on chessboard

Source:

September 10, 2010
LaTeXcombinatorics unsolvedcombinatorics

Problem Statement

Superchess is played on on a 12×1212 \times 12 board, and it uses superknights, which move between opposite corner cells of any 3×43\times4 subboard. Is it possible for a superknight to visit every other cell of a superchessboard exactly once and return to its starting cell ?
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