On Old McDonald's farm, there were only 7 animals left: a chicken, a cow, a donkey, a duck, a goat, a horse, and a pig. Below is a grid representing that farm. The barn is represented by a red square of four cells; the pasture is represented by the green cells; and the blue cells represent the pond.
The cow is in the barn.
The horse is in the pasture.
The duck is in the pond.
These three animals are each the only animal in its respective site mentioned.
Each of the cow, donkey, duck, and pig is in a cell adjacent to the outer square fence.
The pig is directly south of some part of the pasture. (North is at the top.)
No two animals are in the same row or column.
No animal is in the brown farm house.
The animal in the fifth row has more legs than the one in the third row.
The goat's column is further east than the horse's column.
Please tell Farmer McDonald the locations of his seven remaining animals.
Adapted from Readers Digest, May/June, 2025.
If the pig is South of a pasture and adjacent to a fence, then the pig can only be at (4,7)
Since cow, donkey, duck, and pig are along fences, all perimeter rows and columns are accounted for by these 4.
Horse cannot be in Row 1
So Horse in pasture is limited to (2, 456) or (3, 56).
Duck must be either (7,5) or (7,6)
But since Goat is east of Horse, and column 7 is taken, then Goat must be in either column 6 or column 5.
So we have either Horse is (2,4) with Goat in Column 5.
or Horse is (2,45) or (3,5) with Goat in Column 6.
Since Duck and Goat occupy columns 5 and 6, those columns cannot hold any other animals.
The Horse is in (2,4).
The Cow is in (1,1) or (1,2)
(I should have realized here that no animal can be in a corner since that would occupy 2 fences)
(stated another way: "No one puts baby in the corner")
Cow, Horse, Pig, Duck occupy Rows 1,2,4,8 respectively
The North (Cow), East (Pig) and South (Duck) fences are accounted for.
The Donkey must be along the West fence, Column 1.
This fixes the Cow in (1,2) and limits the Donkey to (356, 1).
Reread the clues: only two animals have less than 4 legs, the chicken and the duck. But the duck is in row 7, so the animal in the third row must be the chicken. The only free columns are 1 and 3. But column 1 is a fence so ...
Chicken is at (3,3)
My semi-final answer: not uniquely determined for each animal.
Cow (1,2)
Horse (2,4)
Chicken (3,3)
Pig (4,7)
Goat (5 or 6, 5 or 6)
Donkey (5,1) or (6,1)
Duck (7,5) or (7,6)
unless I assume the Goat will not be in the pond. If that is true then:
Cow (1,2)
Horse (2,4)
Chicken (3,3)
Pig (4,7)
Goat (5, 5)
Donkey (6,1)
Duck (7,6)
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Posted by Larry
on 2025-05-06 15:31:05 |
Verbose Solution
