by **Jean-Christophe** » Fri Sep 08, 2006 11:17 pm

Here is my walkthrough in tiny text you may view by copy-paste to a text editor like notepad

Step 1

The cages layout has 180° rotational symmetry. Thus the cage over R5C5 must have rotational symmetry, with an odd number of cells.

There are two possible shapes : 3 cells in a row (Y 20/3), or 5 cells Z shaped (Y 27/5)

It can't be Y 20/3, because we would be left with only one B 14/3 and only one Y 27/5 which cannot be placed symmetrically in the rest of the puzzle.

Thus it must be Y 27/5 which orientation is like in the list

-> R4C45+R5C5+R6C56 = Y 27/5

Step 2

R5C7 = P (because R4C6 = B, R6C6 = Y, R5C8 = G)

R5C6 must also be P since there is no cage with a single cell.

R5C67 cannot be P 7/2 because symetrically R5C34 cannot be Y 6/2

Thus R5C67 belongs to a larger P cage : either P/3 (L shaped) or P 31/6

R6C7 <> P -> R4C7 = P

Step 3

R6C7 = B -> R6C8 = B

R6C78 is either B 21/3 or B/4, all with an L shape

-> R7C7 = B

R7C6 <> B -> R7C6 = G -> R8C6 = G

Step 4

We have not less than 5 different green cages to place

The given cages are restring their possible locations

-> R234C123 <> G, R456C789 <> G

R78C6 is part of a green cage

Placing the large G 21/6

Trying horizontal orientation like in the list

Not in R789C1234 because it would leave a single cell in R9C1.

Not in R789C2345 because it would touch another G cage in R78C6. And also because symetrically, the P 31/6 can't touch R4C7 which is P.

Not in R789C6789 because it would leave two empty cells in R8C89 and symetrically in R2C12 next to P 31/6. None of them can be P 7/2.

Trying horizontal orientation turned 180°

G 21/6 not in R123C5678, because P 31/6 can't be placed symetrically

There is no other way to place G 21/6 horizontaly

Trying vertically with the long side on the left

Not in R6789C123 because symetrically the P 31/6 can't touch R5C7 which is P

The only place left is in R5678C234

-> R5C34+R6C23+R78C2 = G 21/6

-> R234C8+R4C7+R5C67 = P 31/6

Step 5

We still have to place 4 different green cages

Two of the green cages have a T shape and must be placed symetrically since they are the only 2 ones with a T shape.

A T shaped cage cannot go in N3, because it can't go symetrically in N7

For the same reason, it cannot go in N9 & N1

Thus the 2 T shaped green cage must go in N2, the other in N8 which must include R78C6

-> R23C4 is part of a green cage

R23C3 <> G -> R123C4+R2C5 = G/4 -> R789C6+R8C5 = G/4

Step 6

G 17/4 can't go in N9 -> in N3

G 17/4 can't be placed vertically because it would leave a single empty cell in R4C9

-> R1C789+R2C7 = G 17/4

-> R8C3+R9C123 = Y 18/4

R678C1 = B 14/3, R234C9 = Y 20/3

R8C4+R9C45 = B 21/3, R1C56+R2C6 = P 20/3 (one of the two P 20/3)

R6C78+C78C7 = B/4, R23C3+R4C23 = B/4

R1C1+R2C12 = P 20/3 (the other one), R1C23 = Y 6/2

R8C89+R9C9 = G 21/3, R9C78 = P 7/2

Step 7

We have now placed all the cages and know the sum of all but 4 of them :

The 2 T shaped G/4 : either 15 or 21

The 2 L shaped B/4 : either 17 or 21

Outies of N8 -> R6C4+R7C3 = 24+21 + (15|21) - 45 = 15|21

Max of 2 cells = 17 -> G 15/4 in N8, G 21/4 in N2

R6C4+R7C3 = 15 = {69|78}, R7C45 = 9

45 on N2 -> R3C56 = 4 = {13}, R3C7+R4C6 = 12 = {48|57}

Step 8

Outies of C123 -> R56C4 = 20+6 + (17|21) + 14+14+21+14+15+18 - 135 = 4|8

Since R6C4 = {6789} -> R56C4 <> 4 = 8

-> B 21/4 in N14, B 17/4 in N69

R56C4 = 8 = [17|26] -> R7C3 = {89}

45 on N5 -> R45C6 = 10 = [46|73|82] -> R3C7 = {458}

Step 9

45 on N1 -> R4C123 = 16, R23C3+R3C12 = 19

45 on N9 -> R6C789 = 8 = {134|125} = {1...}, R7C789+R8C7 = 17

45 on R6789 -> R6C56-R5C34 = 14

Min R5C34 = {12} = 3 -> Min R6C56 = 14+3 = 17 = {89} = Max R6C56

-> R5C34 = {12}, R6C56 = {89}

-> R45C6 = [46|73] = {(6|7)...} forms a complex naked pair on {67} with R6C4 -> not elsewhere in N5

Step 10

Cage 21/6 = {123456} -> R6C23+R78C2 = {3456} (BTW -> R45C2 <> {3456})

45 on N4 R5C3+R6C123 = 15

R5C3 = {12} -> R6C123 = 13|14 = {346|347|356}

-> 2 of R6 locked in R6C789 = {125} -> R5C89 <> {57}

-> R5C7 = 7 (hidden single in R5)

45 on R5 -> R5C56 = 9 = [36], R4C6 = 4, R3C567 = [138], R6C4 = 7, R5C34 = [21], R7C345 = [836]

R5C12 = {59}, R5C89 = {48}, R4C9 = 6, R4C78 = {39}, R23C8 = {24}, R23C9 = {59}

R5C89 = [84], R67C9 = {12}, R7C8 = 5, R6C7 = 5

R89C9 = {78}, R8C8 = 6

R1C89 = [73], R12C7 = {16}, R78C7 = {29}, R6C89 = [12], R7C9 = 1, R9C78 = [43], R4C78 = [39]

Cage 14/3 in R3C12+R4C1 = {167} -> R4C123 = [187], R23C3 = [15], R1C23 = [24]

...

Edited to fix a typo

Last edited by

Jean-Christophe on Sun Sep 10, 2006 3:10 pm, edited 1 time in total.