Progress Report:
well if you add all 16 numbers up you get 136. so each of the four
corners groups of 2x2 have to be 34 (136/4) so you logically get the top left
number as 16.
then you use the 9 and the 2 with the empty spaces below. you add 9 and 2
getting 11, therefore the numbers below them have to add up to 23 to get
the total of 34. so the possibilities are 7,16 8,15 9,14 10,13 11,12 rule out
7,16 and 9,14. leaving you with now 8,15 10,13 11,12. but when you add
them with the 1 in the bottom left you get 24, forcing that other number to
be the 10. 8,15 and 11,12 only work now.
now look at the 7 and 2. they add up to 9 meaning the other 2 have to add
to 25. combos that work are 11,14 and 12,13.
neither of those combos work with the 11,12 for the first set we looked at,
because they both have one of the numbers, making the first set the 8 and
15.
16| 7 | 12 | 3
------------
9 | 2 | 13 | 6
----------- you know the numbers to the left of the 3 add to
8 | 15| 4 | 11 25, so those plus 3 is 28, making the other 6.
------------
1 | 10| 5 | ? 14
or
16| 7 | 13 | 3
------------
9 | 2 | 12 | 6
-----------
8 | 15| 5 | 11
------------
1 | 10| 4 | ? 14
or
16| 7 | 12 | 3
------------
9 | 2 | 13 | 6
-----------
15| 8 | 11 | 4
------------
1 | 10| 5 | ? 14
or
16| 7 | 12 | 3
------------
9 | 2 | 13 | 6
-----------
8| 15 | 4 | 11
------------
1 | 10| 5 | ? 14
as you see theres alot of solutions, and im probably missing some. but if you
notice its usually flipping sets of numbers in a row. you cant flip unless the
whole row is empty at the beginning. thats why the 14 cant move. it is in 2
rows with numbers forcing it to stay
that took forever so theres prolly some mistakes or missing parts