How many squares are there in n x3 array with n >=5
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30 tháng 6 2017
thiếu đề bài
dịch thì dịch thế này
Trong hình này, có 8 con chim bồ câu nằm trên một trong mười sáu ô vuông. Ít nhất có bao nhiêu con chim bồ câu cần phải di chuyển từ nơi chúng đến những ô vuông mới (không nhất thiết phải cạnh những ô vuông ban đầu) sao cho chỉ có hai chim bồ câu Trên mỗi hàng, mỗi cột
DU
1
TH
1 tháng 9 2021
Another alternative explanation.
Mark the leftmost square crossed of each row as ‘r’, and the topmost crossed square of each column with ‘c’. Thus, each square can be marked either ‘r’ or ‘c’ or ‘both r and c’ or ‘neither r nor c’. We’ll examine each case.
For a square to be marked both ‘r’ and ‘c’, the diagonal must pass through the upper left corner of the square.
For square to be marked ‘r’, diagonal should pass through its upper edge.
For square to be marked ‘c’, diagonal must pass through its left edge.
For square to be marked neither ‘r’ nor ‘c’, diagonal must pass through it’s upper as well as left edge, which is not possible. Therefore, no triangles are unmarked.
Now, no. of squares crossed = no. of squares marked ‘r’ + no. of squares marked ‘c’ - no. of squares marked both ‘r’ and ‘c’
Now, no. of r’s = no. of rows (only 1 leftmost crossed square in each row)
no. of c’s = no. of columns (only 1 topmost crossed square in each column)
all rows and columns are crossed by the diagonal.
Therefore, squares crossed = rows + columns - (no. of squares marked both ‘r’ and ‘c’)
Now, only 1 square is marked both ‘r’ and ‘c’ as 199 and 991 are coprime.
Therefore squares crossed = 199 + 991 - 1 = 1189
Look at this video if you want a clearer visual explanation:
DU
2
1 tháng 9 2021
Tham khảo:
Another alternative explanation.
Mark the leftmost square crossed of each row as ‘r’, and the topmost crossed square of each column with ‘c’. Thus, each square can be marked either ‘r’ or ‘c’ or ‘both r and c’ or ‘neither r nor c’. We’ll examine each case.
For a square to be marked both ‘r’ and ‘c’, the diagonal must pass through the upper left corner of the square.
For square to be marked ‘r’, diagonal should pass through its upper edge.
For square to be marked ‘c’, diagonal must pass through its left edge.
For square to be marked neither ‘r’ nor ‘c’, diagonal must pass through it’s upper as well as left edge, which is not possible. Therefore, no triangles are unmarked.
Now, no. of squares crossed = no. of squares marked ‘r’ + no. of squares marked ‘c’ - no. of squares marked both ‘r’ and ‘c’
Now, no. of r’s = no. of rows (only 1 leftmost crossed square in each row)
no. of c’s = no. of columns (only 1 topmost crossed square in each column)
all rows and columns are crossed by the diagonal.
Therefore, squares crossed = rows + columns - (no. of squares marked both ‘r’ and ‘c’)
Now, only 1 square is marked both ‘r’ and ‘c’ as 199 and 991 are coprime.
Therefore squares crossed = 199 + 991 - 1 = 1189
SA
14 tháng 7 2017
1..How many.................apples are there in the fridge?
2...How much................pepper do you want?
3....How many..................bananas are there on the table?
4...How many...................sandwiches are there in your bag?
5.....How much..............water is there in the bottle?
30 tháng 3 2020
1 My name is Alice Zuberg
2 A - L - I - C - E
3 I come from SAO alicization
4 I live in Rulid village
5 there are five chair in my house
6 No , I to be alone
7 there are four
8 I come back home and do my homework
30 tháng 3 2020
Okay, i will answer:
1 My name is Nguyen Le Huy ( but my friends only call me Huy )
2 H - U - Y
3 I'm from VietNam
4 I'm live in HaNoi
5 i have a lot of chairs in my house
6 No, cause i don't know who are you,......bruh
7 there are 8 people.
8 i come to my room do my homework
thanks for asking me, stranger. XD
k mình rùi mình giải cho nha !!!!
Giup minh di, minh cho 5
$$$ !^!