Difficult 4x4 Analysis, Monday June 20 2016

This is my first analysis, by the way...

To begin, first we look at column a. The only possibility for the 6+ cage is {2,4} so a1 and a2 must be 1 and 3. Next, we find the values in the 1- cages. Taking into account that the sum of columns b, c, and d is 30 and that the 14+ cage already has 1 and 3 (1+3=4), you can subtract the remaining amount of the 14+ cage and the three rightmost columns (c1+d1+b4+c4=30-10-9-1=10).

This means the 1- cages could {1,2}{3,4} or {2,3}{2,3}. If it was {2,3}{2,3}, then the a column would be as follows: a1=1, a2=3, a3=2, and a4=4. Then looking in the 9+ cage, we can quickly find that {2,3,4} is not possible. This would mean that the 9+ cage is {4,1,4}, which is impossible due to the 1 in d4.

Thus, the lower 1- cage is {3,4} and the upper one is {1,2}. Due to this, a4=2, a3=4, a2=1, and a1=3. This shows b1 to be 4, and the rest of the puzzle can be solved quickly and easily.

Edit by

**pnm**, added puzzle picture: