I really enjoyed the ideas behind this puzzle. Thanks very much for the work you put into making it.
HATMAN wrote:
I avoided using fishes
HATMAN wrote:
This is the conflict move
Thanks for posting your WT but I didn't go past the conflict move. I got the wrong impression about this puzzle.
This is what I could find but couldn't get anywhere useful past this. I used some chains including a short conflict chain (step 8,10)
T = tail.
1. T5 at r7c5 = [1+1+1+2+3/1*1*1*2*3/1*1*1*2*4/1+1+2+2+3] = 8/6/9/9
1a. r7c5 = 1, r6c4 = 1, r4c4 = 2
1b. r6c3 = (12), r3c4 = (34)
1c. r2c3 = (689)
1d. r25c3 = [9/1..]
2. T2 at r4c2; [1+8] = [9] blocked by step 1d -> max. r3c1 = 7
3. T3 at r3c1; [3+2+1/3*2*1] blocked by no 1 or 2 left for r1c1 in T2 at r1c1;[5+2+1/6+2+1] blocked by T2 at r1c1 since max. r3c1 = 7 and must also have 1/2 in r1c1
3b T3 at r3c1 = [4+2+1/4*2*1/4+3+1/4+3+2/5+3+1] = 7..9
3c. r2c1 = (45), r1c2 = (23), r1c3 = (12)
3d. r1c4 = (789)
4. naked pair {12} at r15c3: both locked for c3
5. T2 at r1c1. max. r1c1 = 3 since max. r3c1 = 7
5a. min. r3c1 = 5
6. T2 at r4c2. Min. r3c1 = 5 -> max. r4c2 = 4
6a. must be + since r2c2 <> r3c1 -> min r2c2 = 6
7. T3 at r6c2: max. r8c2 = 2 since min. r7c3 & r6c4 = [3+3] = 6
7a. min. r9c3 = 7
7b. max. r7c3 = 4
7c. max. r8c4 = 5
8. no 3 in r1c1 because it forces r14c2 = [21] which is blocked by r8c2. Like this:
8a. 3 in r1c1 -> T2 at r1c1 = [34] = [7] -> T2 at r4c2 = [17] only with r4c2 = 1
8b. 3 in r1c1 -> r1c2 = 2 -> r14c2 = [21] which is blocked.
9. naked pair {12} at r1c13: both locked for r1 & n1
9a. r1c2 = 3
9b. from 3b T3 at r3c1 = [4+3+1/4+3+2/5+3+1] = 8,9 (no 7 in r1c4)
10. r24c2 must be [9/1] -> 9 locked in r2c23 for n1 and r2 and 1 locked in r4c2 + r5c3. Like this.
10a. if 4 in r4c2 -> T2 at r4c2 = [45] = [9] -> r5c3 = 1 (step 1d)
10a. if 1 in r4c2 -> r2c3 = 9 (step 1d)
11. T2 at r3c7, min. r2c6 = 2 since min. r1c5 = 4
11a. r3c6 = 1 (hsingle n2)
12. T2 at r4c6: min. r34c6 = 1*3 -> min. 3c5 = 3
12a. 2 in n2 only in r2: locked for r2
13. T2 at r3c7; max. r3c7 = 4, max. r2c7 = 7
14. T3 at r4c9; min. = 6 -> r1c6 = (6..9)
14a. min. r2c7+r3c8 = 3 -> max. r4c9 = 6
14b.
14c. max. r3c8 + r4c9 = 8 -> max. r2c8 = 4
14d. min. r4c9 = 3
14e. r4c9+r3c8+r2c8 = [3+2+1/3*2*1/3+3+1/3*3*1/4+2+1/4*2*1/4+4+1/ etc
14f. -> r2c7 = 1
15. naked triple {234} in r3c478: all locked for r3 and 2 for n3
16. r2c1 = 4 (hsingle n1)
16a. r3c1 = (56) (T2 at r1c1)
16b. r4c2 + r3c1 = [15] blocked since it r1c1 must be 1 which would leave no 1 for c3
16c. r4c2 + r3c1 = [16]/45] -> r2c2 = (79)
17. 4 in n2 in r1c5 or r3c4 -> no 4 in r3c7 since T2 at r3c7 must be increasing.
18. 5 in n1 only in r3: locked for r3
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 12 3 12 | 89 456789 6789 | 456789 456789 456789 |
| 4 79 689 | 35678 235678 23567 | 1 35678 35678 |
| 56 5678 5678 | 34 6789 1 | 23 234 6789 |
:-------------------------------+-------------------------------+-------------------------------:
| 356789 14 3456789 | 2 3456789 3456789 | 3456789 13456789 3456 |
| 2356789 2456789 12 | 3456789 3456789 3456789 | 23456789 123456789 123456789 |
| 2356789 2456789 3456789 | 1 3456789 3456789 | 23456789 23456789 23456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 2356789 2456789 34 | 3456789 1 23456789 | 23456789 23456789 23456789 |
| 12356789 12 3456789 | 345 23456789 23456789 | 23456789 123456789 123456789 |
| 12356789 12456789 789 | 3456789 23456789 23456789 | 23456789 123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'
Cheers
Ed