by **jimbob** » Sun Mar 12, 2006 3:57 pm

Sorry, I'll try to explain.

N means nonet, another name for box. So N1 means the top left hand box, N2 means the top centre box, etc. Since cages can cross into more than one box we may need to refer to more than one box for any particular cage.

N23 12/4 cage - this means the cage covering 4 cells, sum 12 contained in nonets (boxes) 2 and 3, ie top centre and right.

The 9-sum cage in column 9 cannot be 1,8 or 4,5 since the 8-sum cage in the same column must contain a 1 and also contain either 4 or 5. Therefore the 9-sum cage must be 2,7 or 3,6. If it was 2,7, then r1c6 must be 2, since the 12-sum cage must be either 1,2,3,6 or 1,2,4,5. But since nonets 3 and 6 must add to 90, r1c6-r6c9=4, so r1c6 cannot be 2.

So the 9-sum cage must be 3,6. This leaves the 8-sum cage to be 5,1,2. Since the 7-sum cage in row 7 must already use 1,2,4 this places the 5 in r7c9.

Since all rows add to 45, the sum of r8 and r9 must be 90. By observing cages in the bottom 2 rows we find that r7c2+r7c8-r8c9=9. We know r8c9 is 1 or 2 (part of 5,1,2 8-sum cage). We also know that the 7-sum cage in row 7 uses 1,2,4. Therefore r7c2 and r7c8 must be 3,7 or 3,8 (depending on the value of r8c9). But c2 must already have a 3 in the N4 4/2 cage.Therefore the 3 must be in r7c8.

[Edited to include extra step omitted originally]

Last edited by

jimbob on Mon Mar 13, 2006 5:38 am, edited 1 time in total.