Hello Community!
I need some help with the problem in the image link above. This is ZIO $2013$ P$3$
The answers are $30,8,17$.
My failed attempt: For the first part, we need even the minimum difference to be large, we need to make the elements as far away and as evenly spaced as possible (just what they did in the example). Moving on part (a), we follow the same strategy. I calculated the difference and found that the leat further away elements were $144$ and $152$ with a difference of $8$, so we need to make them farther away. $152 + 13 = 165 $ and similarly, I added $39 + 13 = 42$ and $117 - 6 = 111$ (otherwise $131$ would get close) but I got answer $20$ which is wrong. Also, we can't guarantee anything this way.
Help would be much appreciated. Thank You.