Projection formula

I use a spreadsheet to do projections based on recent performance and future goals. As data comes in each day I'd like the future numbers to update automatically.

For example, if my first set of numbers are:
10
12
11

and the total goal for the date range is a total of 150, and the last 3 numbers will average out to the same average as the first 3 numbers, and there are 6 numbers in between, we have this:

10
12
11
14
14
14
14
14
14
11
11
11

However if the first 14 actually comes out to 19, when i manually type in the 19 over the 14 I need the other five 14's below it to update automatically to 13 apiece so that it looks like this:

10
12
11
19
13
13
13
13
13
11
11
11

I hope this makes sense and isnt too confusing. There are some other pieces that I left out for now for the sake of simplicity but hope we can get to those later. Looking forward to seeing who is up for the challenge!

No, it will change. The total number of values could change (instead of a constant 12), and the number of values in each of the 3 sets of numbers could change. So the first set might have 7 values, the third set might have 14 values, and the third could have 5 values.

Also, sometimes there will only be one or two sets of numbers. In the case where there are two sets, the third set is eliminated. In the case where there is one set, it will only be the middle set.

Either way, the hard thing to me is getting the middle set to update based on numbers that have manually been entered over the projected value.

Really it doesnt matter how many numbers there are since that will change from time to time but the total stays the same.

The important thing is to change the calculated 14's as they are replaced with manually entered numbers. So in this example, when the first calculated 14 is replaced manually with 19, the other 14's become 13's. Then when the first 13 is replaced with 17, the other four 13's become 12's, etc. so that the total remains at 150:
10
12
11
19
17
12
12
12
12
11
11
11

The first and last three numbers are manually entered, yes. The middle numbers are calculated based on the sum of those numbers and the difference from the total. But the values of those calculated numbers should change as they are manually entered.

And yes, in this case we can assume there are 12 total values and 6 are manually entered and 6 are calculated. So the question is how to get the 6 calculations to change as they are replaced with manually entered values.

I guess if we simplified this further we could just say we have 6 values that total 84. If we start out with a simple 84/6 calculation the values become 14. But if the first 14 changes to 19, the others should become 13. So the calculation is more complex since it should take into account that the other numbers could change. Make sense?

Interesting, but when i change the first 15 to 20 the other 15's dont update. They should change to 14

I figured it out using the sumif formula. Thanks for the help!