Re: Difficult 6x6 Thursday July 21st

paulv66 wrote:

I found it very difficult to get to grips with today's 6x6. It was one of those patterned ones, with a 4x4 central core and 4 L shaped cages around the outside.

I finally worked it out, but it took me longer than it took me to do today's 12x12. Did anyone else struggle with this one, or was it just me?

Hi, paulv66.

Since b5-c5 = [1,3] >>> e4 = 1, e5 = 2. Of course b4-c4 = [5,6]. The cage "3-" in d4-d5 can be [2,5] or [3,6]. You can quickly eliminate [3,6], because then a3 + a4 = 9 (that is, 17 + 4 + 6 + 2 + 22 - 42, being 42 the sum of the two lower rows). Consequently, in this hypothesis, a3 = 5, a4 = 4 and no number would now be possible in a5. Then d4 = 2, d5 = 5. As a consequence d3 = 1, e3 = 4 and d2-e2 = [3,6] (unique).

And this means that cage "4-" must be [2,6] (with c2 = 2, c3 = 6) (because the 4x4 central core has a total sum of 126 - 3 x 17 - 22 = 53, that is, the fulll grid minus the four L-shape cages, producing a sum of 8 for this cage).

At the same time, and similarly as before, now a3 + a4 = 17 + 4 + 5 + 2 + 22 - 42 = 8 >>> a3 = 5, a4 = 3, then f4 = 4 >>> a5 = 4 >>> f5 = 6. And also b4 = 6, c4 = 5.

Clearly, the 3 of row 3 is not possible in b3 so b3 = 2, b2 = 4 (f2 = 3). And f2 = 5, a2 = 1. Since a6 + b6 = 5 >>> a6 = 2, b6 = 3 (obviously a 6 in a6 would have been excessive for the "17+" cage

) and the rest is quickly filled (f1 = 2, f6 = 1, ... ).

Finally, you may observe something that you could find useful in the future: The sum of the corners in this case is 11 (6 + 2 + 2 + 1). As we know (the demonstration is in other places in the Forum), the 4x4 central core has always a sum which is equal to the sum of the corners + 2 complete lines, that is: 53 = 11 + 42 (in a 6x6 puzzle).