Competition problem — Combinatorics

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Combinatorics Difficulty 5.3 AIME, harder Prove it Ukraine

Is it possible to fill in a table $7 \times 7$ with $24$ ones and $25$ zeros so that:
1) for each cell containing one, sum of numbers in neighbour cells equals one,
2) for each cell containing zero, sum of numbers in neighbour cells does not equal one?
(Two cells are neighbours if they have a common side.)

Solution

Answer: Yes, it is possible (see the figure).

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