denis_berthier wrote:Speaking of frequencies, is there an estimate of the ratio JExocet/Exocet (in the "potential hardest" list if there's nothing less biased)?

This post, is meant to address that question.

Statistics for exocets in champagne's Oct 2012 "potential hardest" puzzle list.The list contains 56448 puzzles.

Before searching for exocets, the PMs for puzzles were advanced as far as possible using singles, line/box eliminations, and eliminations from naked and hidden subsets, and basic fish.

No restrictions were placed on the number of base digits, or the positions of the base and target cells.

(Well OK, one restriction: no more than 8 base digits).

At that point, 47575 of the puzzles, contained exocets.

The total number of exocets was 162278.

[ That count, doesn't include exocets that are produced when two "locked quads" for the same digits, overlap in two cells. There were 182 of those.

champagne likes to ignore them, and I'll stick with that approach.

Added: the original search was also restricted to cases with >= 3 base digits. After

champagne noted that there wasn't a column for 2-digit exocets, I expanded the search to include those as well. Only 6 cases were found, 2 each in 3 puzzles. They were cases where a puzzle contained two non-intersecting locked pairs, for the same digit. If I run the search again, I'll include the 2-digit cases, and filter out any cases like that. ]

Below is 1) a breakdown of exocets, by size and type, and 2) a breakdown of puzzles by the "leading (exocet) type".

For the puzzle breakdown, a JExocet of any size, preceded any other kind of exocet, and so on -- then smallest to largest base digit count, for the same "types".

- Code: Select all
` size Exocets`

+------------+-------------------------+

| 3 4 | 5 6 7 8 |

+---+------------+-------------------------+

t | A | 6 52869 | 7 - - - | 52882

y | B | - 2066 | 1655 3937 452 45 | 8155

p | C | 1 47413 | 20 - - - | 47434

e | D | 2 5335 | 14987 1177 - - | 21501

+---+------------+-------------------------+

| G | - 185 | 9811 5574 164 - | 15734

| H | - 135 | 29 - - - | 164

| K | 1 4905 | 4587 6642 135 1 | 16271

| O | 27 40 | 69 1 - - | 137

+---+------------+-------------------------+

37 112948 31165 17331 751 46 162278

- Code: Select all
` size Puzzles`

+------------+-------------+

| 3 4 | 5 6 |

+---+------------+-------------+

t | A | 6 43471 | 2 - | 43479

y | B | - 2022 | 937 1 | 2960

p | C | - 9 | 16 - | 25

e | D | - 686 | 138 1 | 825

+---+------------+-------------+

| G | - 59 | 8 3 | 70

| H | - 56 | 2 - | 58

| K | - 139 | 18 1 | 158

| O | - - | - - |

+---+------------+-------------+

6 46442 1121 6 47575

"Type" definitions:

---- JExocet-like

A) Standard JExocet (with the allowances for "degenerate cases")

B) Like (A), but with the "box singles" extension.

C) Patterns from by previous post, with JExocet conditions satisfied for all digits.

D) Like (B), but with "box extensions" (see previous post).

---- "hard core" exocets

G) Base cells in a mini-row/col, target cells in the base band/stack, targets in different boxes.

H) Base cells in a mini-row/col, target cells in the base band/stack, targets the same box.

K) Base cells in a mini-row/col, at least one target outside the base band/stack.

O) Unrestricted, none of the above.

The counts for some of the "hard core" types, and the size > 4 cases, while accurate, are somewhat of a distortion. A lot of them end up being cases where a template analysis, shows that one of the target cells needs to contain a particular base digit. When that's true, there can be several cells that end up forced to contain that digit, and usually any one of them can be designated as a "replacement" target cell, for the first target. There's nothing wrong with them, as exocets, but they're sort of unsatisfying, once you see what's going on. I filtered out two classes of exocets, and used the results to produce another pair of tables like the ones above. Whether that was the best idea ... who knows. It is what it is.

The classes that were filtered out, were:

1) cases where one of the target cells, only contains a candidate for one base digit.

2) cases where (single digit) template analysis, shows that for all but one of the base digits, if the digit appeared in the base, it would be forced to occupy a particular (common) target cell. When that's the case, only one of those values could appear in the base, and (assuming the exocet is valid), the remaining digit, must go in the 2nd base, and 2nd target cells.

- Code: Select all
`Filtered:`

size Exocets

+------------+-------------------------+

| 3 4 | 5 6 7 8 |

+---+------------+-------------------------+

t | A | 6 51780 | 7 - - - | 51793

y | B | - 2036 | 170 - - 45 | 2251

p | C | 1 46313 | 4 - - - | 46318

e | D | 2 5326 | 14976 1177 - - | 21481

+---+------------+-------------------------+

| G | - 56 | 21 265 164 - | 506

| H | - 62 | 26 - - - | 88

| K | 1 3072 | 29 3 3 1 | 3109

| O | 27 40 | 69 1 - - | 137

+---+------------+-------------------------+

37 108685 15302 1446 167 46 125683

- Code: Select all
`Filtered:`

size Puzzles

+------------+-------------+

| 3 4 | 5 6 |

+---+------------+-------------+

t | A | 6 42393 | 2 - | 42401

y | B | - 1996 | 58 - | 2054

p | C | - 135 | - - | 135

e | D | - 1582 | 328 17 | 1927

+---+------------+-------------+

| G | - 40 | 2 3 | 45

| H | - 4 | - - | 4

| K | 1 157 | 19 1 | 178

| O | - 7 | 39 - | 46

+---+------------+-------------+

7 46314 448 21 46790

Comments and questions welcome.

A note about the "type O" cases: I didn't place any restrictions on the positions of the base cells, but I did require that when they can't see each other, a single digit template analysis shows that the two cells can't hold the same digit. I'll check whether cases like that, ever came up. It doesn't seem likely. (Edit: no, it didn't happen).

Blue.