# The Farmhouse Problem

John Farmer woke up one morning to pandemonium in his barnyard. The gate had been left open and the animals had wandered out during the night. When he looked out the window, he could see the chickens and the sheep. By the time he got downstairs he could see the goats, too. But he had to hunt for the cows and the horses. After an hour of running around, Jake finally got all his animals back in their pens. Using the clues below, determine how many of each animal the farmer had to find, what kind of mischief each type of animal got into, and how long it took the farmer to return each group of animals to their pens.

- The animals running loose on the neighbor’s lawn were not the goats.
- The twelve chickens, who were not eating Jake’s vegetable garden, took the most time to return to their pen.
- Jake had five of one type of animal; he had an even number of all the other animals.
- The animals he had the least number of were the ones found in the grain room. The animals he had the most of took him twenty minutes to catch.
- The animals Jake had only two of took five minutes to catch while the animals he had six of took twice as long to catch.
- Jake had six more chickens than goats but two more goats than sheep.
- It took five minutes more to catch the horses than it took to catch the animals in the hay field but getting the horses took five minutes less than collecting the animals scattered around the barnyard.
- It took Jake the same amount of time to collect the four animals in the hay field as it did to collect the goats.

ANIMAL | Number of animals | Animals’ location | time |

CHICKENS |
|||

COWS |
|||

GOATS |
x | ||

HORSES |
|||

SHEEP |
x |

- Chickens – 12 – Barn yard – 20 min
- Cows – 2 – Grain room – 5 min
- Goats – 6 – Vegetable garden – 10 min
- Horses – 5 – Lawn – 15 min
- Sheep – 4 – Hay field – 10 min

Explanation:

From (2), Chickens = 12

From (6) Chicken = goats + 6. So goats = 6 .

From (6) goats = Sheep + 2. So sheep = 4

From (3) and (5) cows and horses have to be either of 2 or 5.

So maximum number is 12 – chickens

From (4) it took 20 minutes to catch 12 chicken

From (5), It took 10 minutes to catch 6 goats

Using (8) , it took 10 minutes to catch 4 sheep

Using (8) 4 sheep in the hay field took 10 minutes to catch ——————(A)

Using (7), it took 15 minutes to catch the horses

So the 12 chickens in the barnyard took 20 minutes to catch …………………….(B)

Using (5), It must have taken 5 minutes to catch the cows.

Also then cows = 2. So horses = 5

Using (4) 2 cows were in the grain room took 5 minutes to catch……………….(C)

Using (1), 5 horses in the lawn took 15 minutes to catch………………………………(D)

That leaves us with

6 goats in the vegetable garden took 10 minutes to catch ……………………………(E)

### Your Answer

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