sjs34 wrote:

I would be curious to hear from those who did solve today's 9x9 as to what their key maneuvers were.

I used the parity rule to start. For instance:

**g4 + g6 must be even** (parity for the three rightmost columns) since "6x" is odd (with [1,3] or with [1,6]). Consequently [4,8] must be excluded for "12x" due to g4 = 8 >>> g6 = 9 because then g4 + g6 would be 17. Also [3,9] must be excluded because being g4 odd (3 or 9) g6 should be odd, that is, g6 = 9 and then g4 = 3, f4 = 9 and f6 = 8. Observe that in this case "5-" should be [1,6] (unique) with f8 = 1, with the consequence of the impossibility for the cage "6x" because neither [1,6] or [2,3] could be filled (this last due to g4 = 3 and g5 = 2).

So we have arrived to the only "12+" = [5,7] with f4 = 7 and g4 = 5 (well with the addtional d1 = 7). As a consequence, g6 = 9 (to make the even sum with g4 = 5) and f6 = 8. Also "7+" = [3,4] (unique). Observe that "13+" is unique with b3 = 5 and b4 = 8.

Consider now the parity for the three leftmost columns:

**c4 + c6 must be even** and this means that

**d4 + d6 is also even**, right?. Now you can determine (looking to the parity of the three central columns) that the cage "252x" is even ([1,6,6,7] or [2,3,6,7]) and consequently, since "8x" is obviously [1,8], you arrive (considering now the parity for the three upmost rows) to: b3 + h3 even and then h3 = 9 and h4 = 6.

Again with the parity conditions it's very easy to see that d6 = 6 and consequently, to make the even sum, d4 = 4 (c4 = 3) (c6 has the candidates 5 and 7) because [5,6] or [6,7] are the only allowed possibilities for "1-" (c6-d6) (it's very easy to see that [2,3], [3,4] or [4,5] are not possible and, logically, [1,2], [7,8] or [8,9] are forbidden). Etc. ... the full solution is extense.

Perhaps this helps.

Reedit. Another tips: The sum of the content of the cages "2-" (h6-h7) and "6x" is 13. Also more parity conditions:

**b7 + h7 is even** (considering the parity for the three bottom rows) and, consequently, b6 + h6 is even. After the first steps mentioned I went (in a similar way as sneaklyfox) to determine that "2-" (h6-h7) is [3,5] (being impossible [2,4] when the possibilities for the three bottom rows are analyzed).

Reedited to add a clarification.