eclipsegirl wrote:

I just wanted to congratulate the 97 people who solved it.

It was tough.

I loathe the particular pattern. It is the hardest of the various 9 x 9 patterns.

Its been a very long time since we have seen that pattern.

At the beginning I was scared of the puzzle, when I saw the pattern and the difficulty level (121!), and I was absolutely stuck once filled the "obvious" cells. Every cage had multiple possible combination, especially the multiplication ones on the left (columns a, b, c, d).

At a certain point I remembered a way to approach the diagram not so common, which I had read in one of the introductions in the Patrick’s books: you can’t only use the “addition” tool (every column or row has 45 as sum of the first 9 numbers) but also the “multiplication” tool: every column or row has 1×2×3×4×5×6×7×8×9 = 9! as product of the first 9 numbers, so two columns have (9!)^2, three columns have (9!)^3 and so on. These are huge numbers, but getting the number of the first three columns (9!)^3 and dividing it by the three products in there and the other numbers already inserted, I got a “small” product that, divided in factors, gave me a smaller number of possible combinations for the remaining cells of the columns a, b, and c. Above all, combining the “multiplication” way with the “addition” one, I got very few possibilities for the two 3024× and 180×. Just two for the 3024× and two for 180×.

I put the two for 3024× randomly in both cages, but soon I understood that it was the wrong choice, so I inverted the two combination (at that point the 180× was unique) and went on. I can’t say that at this point it was “easy”, but at least it was more manageable… so, at the end I succeed within midnight of Tuesday! I couldn’t believe it (and I can’t believe it till now!

)