As shown in a lower figure, the integer was clockwise arranged in order from 1.
The located integer will be expressed with which direction of what round it is.
For example, 30 is the number of the northeast of the 3rd round.
Answer the following questions.
(1) With which direction of what round is 64 located ?
(2) Find the number of the northwest of the 10th round.
(3) It was 4160 when numbers of the northwest, northeast, southeast, and southwest of a certain round was added.
Find the number of the southeast of this round.
Answer
(1) the number of the southeast of fourth round
(2) 440
(3) 1024
Solution
(1) 1st round = 4 = 2 × 2
2nd round = 16 = 4 × 4
3rd round = 36 = 6 × 6
4th round = 64 = 8 × 8
(2) 1st round = 1 = 1 × 1
2nd round = 9 = 3 × 3
3rd round = 25 = 5 × 5
Then 11th round = 21 × 21 = 441
The number of northwest = 441 - 1 =440
(3) Sum of 1st round = 2 + 4 + 6 + 8 = 20 = 5 × 4 = 5 × 4 × 1
2nd round = 12 + 16 + 20 + 24 = 72 = 9 × 8 = 9 × 4 × 2
3rd round = 30 + 36 + 42 + 48 = 156 = 13 × 12 = 13 × 4 × 3
4160 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 13 = 65 × 64 = 65 × 4 × 16
4160 is sum of 16th round.
16 × 2 = 32
32 × 32 = 1024
