若把數字1 至2026 按下圖方法排列。若數字26 位於第6 行第1 個，請問數字2026 位於第幾行第幾個?
1 4 5 16 17 …
2 3 6 15 18 …
9 8 7 14 19 …
10 11 12 13 20 …
25 24 23 22 21 …
26 … … … … …
若把數字1 至2026 按下圖方法排列。若數字26 位於第6
2009-01-23 7:38 am
回答 (2)
2009-01-23 8:04 am
✔ 最佳答案
根據結構n^2的位置必為a1n或an1若n為奇﹐則n^2的位置在an1
若n為偶﹐則n^2的位置在a1n
45^2<2026
而45^2=2025在a45,1
故2026在a45,2
即數字2026 位於第45行第2個
2009-01-23 00:05:04 補充：
如9在a31
16在a14
2009-01-23 01:03:09 補充：
係BOR﹐因為個模式是N=奇數的話﹐則N^2在an1﹐而N^2+1在a(n+1),1
故2026在a46,1
即數字2026 位於第46行第1個
sorry for my mistake
2009-01-23 8:19 am
1
2 3 4
9 8 7 6 5
10 11 12 13 14 15 16
Let n be the row number.
No of numbers in row n = 2*n-1
Total number of numbers up to and including row n
= (2*n -1 + 1) * n /2
= n*n
n*n >= 2026
n >= 45.011
n = 46
Since n is even, the numbers go from left to right.
when n=45, n*n = 2025
So, 2026 is at first (leftmost) position of row 46
2 3 4
9 8 7 6 5
10 11 12 13 14 15 16
Let n be the row number.
No of numbers in row n = 2*n-1
Total number of numbers up to and including row n
= (2*n -1 + 1) * n /2
= n*n
n*n >= 2026
n >= 45.011
n = 46
Since n is even, the numbers go from left to right.
when n=45, n*n = 2025
So, 2026 is at first (leftmost) position of row 46
參考: Myself
收錄日期: 2021-04-26 13:04:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090122000051KK01995