I thought yesterday’s difficult Killer was one of the most difficult in a long time. I found it really difficult to get a hook into it and thought at one stage that I was never going to solve it. I note that it has only been solved 120 times compared to an average of almost 300 for the four previous Fridays.

I agree, probably one of the hardest we have had for awhile.

My suggestion for solving this puzzle would be to look for cages that have a direct relationship to other cages, include the implied cages that can be found by adding cages. These connections can be very helpful when eliminating values.

Implied cages are the result of adding cages, for example by adding the cages in the lower left box we can find that b7+c7=5, we can think of this as an extra cage that can help to solve the puzzle. This is a simple example that does not really need to be thought of as an extra implied cage, but it is a useful technique for when the cells are not together, or if there are several cells to think of as an implied cage.

This puzzle has several implied cages, and it helps that some of them overlap each other. A lot of the progress I made in solving this puzzle relied on considering the implied cages and the way they connected to each other and to the other cages around them.

I agree with Michael E has written.

One is also able to easily show the B4 + E4 = 17, and that forces C1 = {2, 3}

I think that may have been where I started my T & E on Friday.

That is a good example of where considering the overlap of an implied cage helps. If you consider cage c1 (13+) after finding c1=2,3 then any value is possible in the other 2 cells in the cage. If you consider cage c1 together with cage d3 (22+) and with the implied c1/e4 (11+) we can eliminate 1,5 & 9 from the c1 cage. This is a basic example, but this method can be more useful with regions of the puzzle with several overlapping implied cages, like cell g7 that has 3 overlapping implied cages, and is aligned with another implied cage on the same row.

Having said all of that I would guess it was much quicker to solve the puzzle with trial and error, but I prefer not to, and it took me a long time to find the solution.