Updated to complete answer
18th May, 2016
I believe the answer to part 1 is
I suspect the hint is talking about
the Mastermind board game
which means that the numbers on the right for each line
indicate how many of the number on the left of the row are 1) correct but in the wrong position or 2) correct and in the correct position. Analysing these should give the correct values for the last row
So, starting with row 5:
We have a 2 on the right hand side, so one number is in the correct position, and the other two are wrong. Either the first digit of the hidden code is 1, the second is 9, or the third is 4. Lets assume 4 is the correct one (since that's the one we have most other information about). That means neither 1 or 9 are in the code.
Then based on row 1:
4 is correct, but in the wrong position, and neither 2 or 7 are in the code.
From row 3:
we already know 4 is in the wrong position, but so is either 3 or 6. 6 is in the last position in both rows 2 and 3, but it can't be right in one but wrong in the other. So 6 is out, and 3 must be the other correct but misplaced digit.
That means that row 4:
is telling us that 3 is in the second position. Which we already knew, since it's not the third (that's 4) and not the first (it was in the wrong place on row 3). So 2 and 8 are out.
And since we now know what the last two digits are, row 2
must be telling us that 5 is correct in the first position. So we have 534 as the answer for the missing row 6.
Take the answer from part 1, and
This took a while, but think I finally have it based on @ExcitedRaichu's hints in the comments. The answer to part 1 isn't actually 534,but V III IV. Taking the first character and putting it at the end gives III IV V, but then formatting that as XXX X X X gives III I V V, or 3 1 5 5. Add 1 to each digit to get 4266.
If that's a square, then
The diagonal also equals the radius. So sqrt(2)*(x+1000) = r. So take r from Part 2, divide it by sqrt2, and subtract 1000.
The result from part 3 should
give us 4 digits before the decimal point as the year, the first after as the month, and the next two the day. 4266/sqrt(2) gives 3016.517529... Subtract 1000, and we get 2016.518 when rounded to 3 decimal places (or 2016.517 truncated). Which based gives us a date of 18th May, 2016.