Harder Mathematical Problems

• Each digit must be used exactly once.
• The only allowed operation is addition.
• Two single digits may be combined to form a number (so, for example, 2 and 4 may be combined to 24 or 42).
• Two single digits may be combined to form a fraction (so, for example, 2 and 4 may be combined to ²/₄ or ⁴/₂).

       . . 9 / 6 . 8 . . . \ . 5 3
               . . . 2
               -------
                 . 9 . .
                 . . 4 .
                 -------
                   . . 4 .
                   . . . .
                   -------
                         0

           6 . .
           . . . ×
           --------
           . . .
       . . . . 0
     . 5 . 5 0 0 +
     -------------
     . . 5 . 4 .

       . . . / . . . . . . . . \ . . 8 . .
                 . . .
               -------
                   . . . .
                     . . .
                   -------
                       . . . .
                       . . . .
                       -------
                             0

But assume that there is a maximum stake for the roulette, which means that you can only stake n consecutive times with this trick.

• The replacement resistance of two serial connected resistances
  
  is 2 Ohm (R_replacement = R₁ + R₂, where R₁ = R₂ = 1).
  
  
• The replacement resistance of two parallel connected resistances
  
  is 1/2 Ohm (1/R_replacement = 1/R₁ + 1/R₂, where R₁ = R₂ = 1).

• The lengths of the sides are whole numbers.
• The circumference is the square of a whole number.
• The area is a whole number to the power of three.

EVE/DID = 0,TALKTALKTALKTALK...

4... = 4 × ...4

• When the cow and the goat graze on the field together, there is no more grass after 45 days.
• When the cow and the goose graze on the field together, there is no more grass after 60 days.
• When the cow grazes on the field alone, there is no more grass after 90 days.
• When the goat and the goose graze on the field together, there is no more grass after 90 days also.

The goal is to complete the cross-number puzzle on basis of the next hints. In each box of the cross-number puzzle, one digit (0-9) must be placed (and none of the numbers starts with the digit 0).

Horizontal:

1. The area of Dog's Mead (in square yards).
5. The age of Martha, the aunt of farmer Dunk.
6. The difference between the length and width of Dog's Mead (in yards).
7. The number of roods in Dog's Mead multiplied by 8 vertical.
8. The year in which the Dunk family became owner of Dog's Mead.
10. The age of farmer Dunk.
11. The year in which Mary was born.
14. The circumference of Dog's Mead (in yards).
15. The walking speed (in miles per hour) of farmer Dunk, to the power of three.
16. 15 horizontal minus 9 vertical.

1. The value of Dog's Mead (in shillings per rood).
2. The square of the age of the mother-in-law of farmer Dunk.
3. The age of Mary, the daughter of farmer Dunk.
4. The value of Dog's Mead (in pounds).
6. The current age of Ted, son of farmer Dunk, who will be in 1945 twice as old as his sister Mary will be in that year.
7. The square of the width (in yards) of Dog's Mead.
8. The number of minutes in which farmer Dunk walks 1¹/₃ times around Dog's Mead.
9. 10 vertical divided by 10 horizontal.
10. See 9 vertical.
12. The sum of the digits of 10 vertical plus 1.
13. The number of years that Dog's Mead is owned by the Dunk family.

1 rood = 1210 square yards.
1 mile = 1760 yards.
1 pound = 20 shillings.

• Each digit must be used exactly once.
• The allowed operations are: addition, substraction, multiplication and division.
• digits may not be concatenated (so, for example, it is not allowed to use 1 and 4 as 14).
• Brackets are allowed.