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Table Partition Trial (Posted on 2016-07-24)

Can a 75x75 table (consisting of 75x75 identical square grids) be partitioned into dominoes (1x2 rectangles) and crosses (five square figures consisting of a square and its four neighbors.)

Provide adequate reasoning for your answer.

Source: St. Petersburg City Mathematical Olympiad (Russia)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

D1 argument

| Comment 1 of 3

A pretty standard parity argument:

Color the table in chessboard fashion with the corners black and alternating with white. There will be one more black than white. Call this excess (+1).

Dominoes have equal numbers of black and white (0).

Crosses are either center white with 4 black (+3) or center black with 4 white (-3).

Clearly there is no way any number of dominoes and crosses can bring the count to (+1)

Posted by Jer on 2016-07-24 12:10:20

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