Explanation : 17-ന്റെ കൂടെ നമ്മുടെ കൈയിലുള്ള സംഖ്യകളിൽ നിന്ന് 8 കൂട്ടിയാൽ മാത്രമേ പൂർണ വർഗ്ഗം ആകാൻ പറ്റൂ . അതുപോലെ 16-ന്റെ കൂടെ 9 മാത്രമേ കൂട്ടാൻ കഴിയു. അതിനാൽ 16 ഉം, 17 ഉം അറ്റത്ത് ആയിരിക്കണം. തുടർന്ന് മറ്റുള്ള സംഖ്യകൾ എഴുതാം
The pattern will emerge if you notice that 17 can only pair with 8 and 16 can only pair with 9. So 16 and 17 have to be at the ends. Then attack from the ends.
Best Explanation :Pranav DP The basic idea is each number would have two adjacent numbers to pair with, except the two ends. Key is starting with the highest numbers.
Starting with 17, since the sum can only go up, the perfect square it can reach is 25 is by adding 8. Next is 36, which would require 19, but our list don’t have it. (17 8)
Next 16, needs 9 to get to 25 and nothing else is possible. Since both 17 and 16 can be paired with one number, they would be at the two ends.
Moving on with 15. It can go to 16 by adding 1 and to 25 by adding 10 (16 9).
Similarly this pattern repeats. For 14, 13 etc.
1 15 10
2 14 11
3 13 12
Now next 12 is already taken. But it needs one more number (other than 13), which would be 4 to reach 16. So extending our pattern:
3 13 12 4
2 14 11 5
1 15 10 6
Next is just putting these sets together.
6 with 3 to give 9. (1 15 10 6 — 3 13 12 4)
4 to 5 to give 9. (1 15 10 6 3 13 12 4 — 5 11 14 2)
2 needs 7 to go 9. And combinign this with the two ends (17 8 and 16 9) we get the answer!
