The numbers 1 to 9 are to be placed once in every row, column, long diagonal, 3x3 grid and irregular shape (or cage). From the given starters can you complete the puzzle?

I named the columns A-I from left to right, and the rows 1-9 from top to bottom, for reference. To keep myself from getting TOO wordy, I'll be describing my process in the following shorthand:

Region to focus on + key cell values in surrounding area = conclusion.

Ok, here goes. The first group can all be figured out directly from the given information.

Top-right grid + dark blue 2 in G4 = H3 is a 2
Light blue cage + 4 in A6 = E5 is a 4
Red cage + 1 in I1 and 1 in D4 = G5 is a 1
Row 6 + light blue 8 in F7 = B6 is an 8
\ diagonal + top-left grid's 3 in B3 and center grid's 3 in E6 = G7 is a 3
Green cage + 8 in F7 = G8 is an 8

Middle-right grid + 4s in A6, E5, I7 = H4 is a 4
Middle-left grid + 1s in D4 and G5 = C6 is a 1
Light yellow cage + 8s in F7 and G8 = C9 is an 8
Row 6 + 2s in G4 and I9 = D6 is a 2
Row 6 + 6 in H5 = F6 is a 6
\ diagonal + 5s in B9 and G1 = C3 is a 5
\ diagonal + 8 in B6 = A1 is an 8
\ diagonal + only B2 is unfilled = B2 is a 7
Dark yellow cage + 8s in A1 and B6 = D5 is an 8
Middle-right grid + 8s in B6 and D5 = I4 is an 8
Middle-right grid + 3 in E6 = I5 is a 3
/ diagonal + 5s in B9 and G1 = F4 is a 5
/ diagonal + 8s in C9 and G8 = H2 is an 8
/ diagonal + 3s in B3 and G7 = A9 is a 3
Top-right grid + 3s in G7 and I5 = H1 is a 3
Top gray cage + 3s in H1, B3, E6 = F2 is a 3
Middle-left grid + 3s in A9, B3, I5 = C4 is a 3
Bottom-middle grid + 3s in A9, G7, E6, F2 = D8 is a 3
Middle-left grid + 5s in B9, C3, F4 = A5 is a 5
Light yellow cage + 5 in B9 = I8 is a 5
Middle-right grid + 5s in G1 and I8 = H6 is a 5
Top gray cage + 5s in G1 and C3 = E2 is a 5
Bottom-middle grid + 5s in B9, I8, E2 = D7 is a 5
Top-middle grid + 8s in A1, D5, F7 = E3 is an 8
Top-middle grid + 1s in D4 and I1 = F3 is a 1
Top-left grid + 1s in I1, F3, C6 = A2 is a 1
Row 2 + 2s in D6 and H3 = C2 is a 2
Middle-left grid + 2s in C2 and G4 = B5 is a 2
Bottom-right grid + 6 in H5 = G9 is a 6
/ diagonal + 7 in B2 and 9 in H8 = B8 is a 6
Bottom-middle grid + 6s in B8 and G9 = E7 is a 6
Middle-left + 6s in B8 and H5 = A4 is a 6
Top-left grid + 6s in A4 and B8 = C1 is a 6
Pink cage + 6s in C1 and A4 = D2 is a 6
Top-right grid + 6s in D2 and G9 = I3 is a 6
Middle-left grid + 7 in B2 = C5 is a 7
Center grid + 7 in C5 = E4 is a 7
/ diagonal + 7 in C5 = G3 is a 7
Middle-right grid + 7 in G3 = I6 is a 7
Middle-left grid + only B4 is unfilled = B4 is a 9
Center grid + only F5 is unfilled = F5 is a 9
Middle-right grid + only G6 is unfilled = G6 is a 9
/ diagonal + only C7 is unfilled = C7 is a 9
Top-left grid + 9 in B4 = A3 is a 9
Top-right grid + 9 in G6 = I2 is a 9
Top-left grid + only B1 is unfilled = B1 is a 4
Bottom-left grid + 4s in A6 and B1 = C8 is a 4
Top-right grid + only G2 is unfilled = G2 is a 4
Row 3 + only D3 is unfilled = D3 is a 4
Bottom-middle grid + 4s in D3, E5, C8 = F9 is a 4
Column B + only B7 is unfilled = B7 is a 1
Bottom-right grid + 1 in B7 = H9 is a 1
Bottom-middle grid + 1s in H9 and F3 = E8 is a 1
Row 7 + only A7 is unfilled = A7 is a 2
Bottom-middle grid + 2 in I9 = F8 is a 2
Top-middle grid + 2s in D6 and F8 = E1 is a 2
Bottom-left grid + only A8 is unfilled = A8 is a 7
Bottom-right grid + only H7 is unfilled = H7 is a 7
Bottom-middle grid + 7 in E4 = D9 is a 7
Column F + only F1 is unfilled = F1 is 7
Top-middle grid + only D1 is unfilled = D1 is a 9
Bottom-middle grid + only E9 is unfilled = E9 is a 9

Hopefully you were able to follow along with that. So the solution is

8 4 6   9 2 7   5 3 1
1 7 2   6 5 3   4 8 9
9 3 5   4 8 1   7 2 6

6 9 3   1 7 5   2 4 8
5 2 7   8 4 9   1 6 3
4 8 1   2 3 6   9 5 7

2 1 9   5 6 8   3 7 4
7 6 4   3 1 2   8 9 5
3 5 8   7 9 4   6 1 2

Time consuming but fun!

Edited on November 8, 2006, 7:16 pm

Posted by nikki on 2006-11-08 19:10:56