This is not a puzzle, this is a question about a certain puzzle, Dog's mead. Several forms of this puzzle have been known, and I'm referring to this particular form. There are some history on that page of researching for authorship of the puzzle, and how many, slightly varies versions came to be. The author of the puzzle is Bill Williams.
1. Area of Dog's Mead in square yards
5. Age of Farmer Dunk's daughter, Martha
6. Difference in yards between length & width of Dog's Mead
7. Number of roods in Dog's Mead times nine down
8. Year that Little Pigley came into occupation by the Dunks
10. Farmer Dunk's age
11. Birth year of Farmer Dunk's youngest child, Mary
14. Perimeter of Dog's Mead in yards
15. Cube of Farmer Dunk's walking speed in miles per hour
16. Fifteen across minus nine down
1. Value of Dog's Mead in shillings per acre
2. Square of Farmer Dunk's mother-in-law's age
3. Mary's age
4. Value of Dog's Mead in pound sterling
6. Age of Farmer Dunk's son, Ed, who will be twice as old as Mary next year
7. Width of Dog's Mead in yards squared
8. Length in minutes Farmer Dunk needs to walk one and one-third times around Dog's Mead
9. See ten down
10. Ten across times nine down
12. One more than the sum of the digits in puzzle column two
13. Length of tenure in years of Little Pigley by the Dunk family
I have not found the solution to this particular version anywhere on the internet, solutions to other variations, are available, however I think I was able to solve it myself. My question is about the information missing from this puzzle, that is required to solve it. Many versions of that puzzle given in the internet provide many hints, some of which are not necessary for puzzle solution, but some of them seems to be crucial, e.g. it is not possible to solve the puzzle without this information. I would like your help to figuring out which of these hints really need to be added to the problem statement, which are "nice to have to prove you are on the right track", and which are completely unnecessary. I understand that the "nice to have" part is somewhat subjective, but the rest of it I think we can do.
There are some basic information given, that I think is necessary:
20 shillings = 1 pound sterling
1 acre = 4840 square yards
1 rood = ¼ acre
1 mile = 1760 yards
The rest of the post is under spoiler for the sake of those who want to try the puzzle by themselves first.
- Hint: no number in the grid can start with 0. This seems to be crucial, if you allow 0 as the first digit you cannot really bootstrap the solution.
- Hint: All calendar years in the puzzle are roughly contemporary. This can be an alternative to the previous hint. If you know that the year of birth (11 across) starts with 1, you can bootstrap the puzzle. I think that with some reasoning you can rule out 2, and since 0 and 3-9 would not be "contemporary" this hint would work.
- Hint: You probably should at least be told that dog's mead is a rectangular plot of land In my opinion, this is not required. The clues talk about length and width, which makes it obvious.
- Hint: One number in the puzzle in the area of Dog's Mead in roods, but it related to something in the puzzle quite different from that area. I think that this one is a "nice to have". It is not required to solve the puzzle but it can be used to prove that you are "on the right track". Specifically, this is number 32, the age of Martha (5 across).
- Hint: Also, one of the number across is the same as one of the number down. This is number 792 which is 14 across as well as 10 down. Now it seems, like this hit is almost the must, otherwise the farmer's age could be both 72 and 62. If he is 62, one could argue that fathering the first child at the age of 17 is too young, but it is possible, so it looks like this hint is a must to make the puzzle unambiguous.
- Hint: Current year is 1935. In my view this is completely unnecessary, you can deduce this from the rest of the information given.
- Hint: Everyone's age is given assuming that they've already had their birthdays this year. This may sound obvious, but to me, this is necessary to state to avoid age ambiguity. Otherwise the age may differ by one and the puzzle won't have a unique solution.
- Hint: All number in the grid are integers. This seems obvious and unnecessary. On the other hand, stating that all the number in the puzzle are integers, may be necessary, since a fraction multiplied by an integer as some clues ask, can give an integer.
- Hint: No more than one numeral goes in each square. Not sure about this one. It seems usual for cross-number to always have this rule, but if you see such a puzzle for the first time, may be this needs to be told explicitly?
- Hint: Edward is the eldest child, Mary is the youngest, and Martha is in the middle. This seems necessary, otherwise Martha's age is ambiguous. Either this, or we have to assess the hint above about the area of Dog's Mead in roods (32) as necessary.