All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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.)

Source: St. Petersburg City Mathematical Olympiad (Russia)

 No Solution Yet Submitted by K Sengupta No Rating

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

 Search: Search body:
Forums (0)