In the continuation of this array of positive integers, in which column is the number 12 000?
1 | 2 | 9 | 10 | 25 | 26 |
4 | 3 | 8 | 11 | 24 | 27 |
5 | 6 | 7 | 12 | 23 | 28 |
16 | 15 | 14 | 13 | 22 | 29 |
17 | 18 | 19 | 20 | 21 | 30 |
36 | 35 | 34 | 33 | 32 | 31 |
Options:
1. 99
2. 100
3. 101
4. 102
5. 103
Thanks in advance for the help!
Here's my best attempt
It appears that all even squares - except 1 - will terminate in the 1st column
The next perfect square after 12000 is 12100
The square root of 12100 is 110
So....we will have a square that will have 110 integers on each side
12100 will be in the 1st column.....
12109 will be in the second column = 12100 - 12109 + 1 = 2
12108 will be in the 3rd column = 12100 - 12108 + 1 = 3
So.....to find the column containing 12000 we can evaluate this
12100 - 12000 + 1 =
100 + 1 =
101