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Francesco Franchini (Q43375755) From Wikidata Jump to navigation Jump to search No description defined edit Language Label Description Also known as English Francesco Franchini No description defined Statements instance of human 0 references sex or gender male 0 references given name Francesco 0 references date of death 1559 Gregorian 1 reference inferred from Category:1559 deaths retrieved 28 November 2018 place of death Massa Marittima 1 reference imported from Wikimedia project English Wikipedia religion Catholic Church 1 reference imported from Wikimedia project English Wikipedia   Sitelinks Wikip

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5 1 It's possible to cover a 7x9 rectangle using 0 2x2 squares and 21 L-shaped trominos, for example: abbcddeef aabccdeff gghiijjkk glhhimjnk lloppmmnn qoorpstuu qqrrssttu It's also possible to cover it with 3 2x2 squares and 17 L-shaped trominos, for example: aabbccdee fagbcddee ffgghhijj kkllhhiij kklmmnnoo ppqrmsnot pqqrrsstt However, it is not possible to use more than 3 2x2 squares, that is, the remaining four combinations don't work: 6 2x2 squares and 13 L-shaped trominos 9 2x2 squares and 9 L-shaped trominos 12 2x2 squares and 5 L-shaped trominos 15 2x2 squares and 1 L-shaped tromino ...at least this what I got using brute force (a simple C program based on backtracking). I tried to give a mathematical proof for this, but I couldn't. Please help me