# The problem with the five farms

In the spirit of the so-called Einstein Riddle, I think everyone should try to create their own version. So here is mine:

Five farms are next to each other along a country road (like in the next picture). Let's call them Farm #1, #2, #3, #4 and #5 counting them from left to right.

Their owners are Alice, Ben, Grace, John and Peter. Each one has different crops on his farm, rye, barley, corn, soy beans and wheat, and each one harvested the crops on a different month of last year (from May to September). The one with less employees, has 5 of them and the one with more has 9. Everyone has a different number of employees. Finally, each farm has their own type of fence: one has fences made of wire , other has fences made of wood, another one has fences made of metal, another one has fences made of rocks and another one has fences made of bricks.

The goal is to fill the next table:

    | Farm:          |   Farm #1   |   Farm #2   |   Farm #3   |   Farm #4   |   Farm #5   |
========================================================================================
| Owner:         |      ?      |      ?      |      ?      |      ?      |      ?      |
| Crop:          |      ?      |      ?      |      ?      |      ?      |      ?      |
| Harvest month: |      ?      |      ?      |      ?      |      ?      |      ?      |
| Employees:     |      ?      |      ?      |      ?      |      ?      |      ?      |
| Fences:        |      ?      |      ?      |      ?      |      ?      |      ?      |


by using the following hints:

1 . Ben has 6 employees and is Alice's neighbor.
2 . Peter grows wheat and harvested it on September.
3 . The fence on John's farm is made out of bricks.
4 . The person who harvested in July has 5 employees.
5 . Grace lives one to the right to the farm with wire fences.
6 . 17 employees work on the first two farms.
7 . Alice farm's fences are made out of metal and are quite next to the wood fences.
8 . The person who grows soy beans has less than 7 employees.
9 . The rye grows on a farm with rock fences.
10 . The barley was harvested right after the corn.
11 . It takes 12 employees to harvest the corn and the rye.
12 . Alice has 7 employees.
13 . The person who harvested in June, did it with 8 employees right next to the wood fences.

The table:

| Farm:          |   Farm #1   |   Farm #2   |   Farm #3   |   Farm #4   |   Farm #5   |
========================================================================================
| Owner:         |    John     |    Peter    |    Alice    |     Ben     |    Grace    |
| Crop:          |   Barley    |    Wheat    |    Corn     |     Soy     |     Rye     |
| Harvest month: |    June     |  September  |     May     |    August   |    July     |
| Employees:     |      8      |      9      |      7      |      6      |      5      |
| Fences:        |    Brick    |    Wood     |    Metal    |     Wire    |    Rock     |

Reasoning:

Starting off with an initial of each option in each category and then eliminating the obvious ones from the points (for initials with the same later, whichever comes first is italic):

| Farm:          |   Farm #1   |   Farm #2   |   Farm #3   |   Farm #4   |   Farm #5   |
========================================================================================
| Owner:         |     JP      |     JGP     |    ABJGP    |    ABJGP    |    ABJGP    |
| Crop:          |     bw      |     bw      |     rcs     |     rcs     |     rcs     |
| Harvest month: |    mjas     |    mjas     |    mjjas    |    mjjas    |    mjjas    |
| Employees:     |     98      |     98      |     765     |     765     |     765     |
| Fences:        |    wwmrb    |    wwmrb    |    wwmrb    |    wwmrb    |    wwmrb    |

We know there are 9/8 employees on farm 1 and 2 from point 6. This means that Alice and Ben cannot work on these farms, and Grace cannot work on farm 1 as she is to the right of someone. The number of employees also means points 4, 8, 11 and 13 can eliminate various other possibilities. Barley and wheat are the crops of the first two, so they can't be the crops of the rest.

Now we can look at the fields with less options:

| Farm:          |   Farm #1   |   Farm #2   |   Farm #3   |   Farm #4   |   Farm #5   |
========================================================================================
| Owner:         |     JP      |     JGP     |    ABJG     |    ABJG     |    ABJG     |
| Crop:          |     bw      |     bw      |     rcs     |     rcs     |     rcs     |
| Harvest month: |     js      |     js      |     mja     |     mja     |     mja     |
| Employees:     |     98      |     98      |     765     |     765     |     765     |
| Fences:        |    wmrb    |    wwmrb    |    wwmrb    |    wmrb     |     mrb     |

Point 2 tells us Peter grows the wheat in september, so peter and september can be eliminated from farms 3, 4 and 5. Peter must also have 9 employees, as he harvested in september and the person who harvested in June had 8. They person who harvested in June must have harvested barley, which means corn was harvested in may as it was a month before. Whoever grows soy beans also must have 6 employees, as it takes 12 for corn and rye, and the only combination to make 12 with numbers 5-9 is 7 + 5.

As Alice has 7 employees and metal fences, she must grow corn, as rye has rock fences. Rye is harvested in July by someone with 5 employees and a rock fence. Therefore, only Grace could have grown Rye, as everyone else has something which doesn't match.

Using these deductions:

| Farm:          |   Farm #1   |   Farm #2   |   Farm #3   |   Farm #4   |   Farm #5   |
========================================================================================
| Owner:         |      J      |      P      |      A      |      B      |      G      |
| Crop:          |      b      |      w      |      c      |      s      |      r      |
| Harvest month: |      j      |      s      |      m      |      a      |      j      |
| Employees:     |      8      |      9      |      7      |      6      |      5      |
| Fences:        |      b      |      w      |      m      |      w      |      r      |

Info for each person so far:

- Alice grows corn in May with 7 employees with a metal fence. Neighbours Ben and wood fence.
- Ben grows soy in August with 6 employees. Neighbours Alice, wood or wire fence.
- Grace grows Rye in July with 5 employees and a rock fence. To the right of wire.
- John grows Barley in June with 8 employees and a brick fence. Neighbours wood fence.
- Peter grows wheat in September with 9 employees, wood or wire fence.

To order them, points 1, 5, 7 and 13 are key. We know that wood neighbours Alice and John, Grace is to the right of wire, and Ben is next to Alice. This means Ben must be wire, as if John is wire then Grace is to the right of him and hes not next to Alice. The order must then be J - P - A - B - G and we have completed the puzzle!

• I didn't make it hard enough... :) Well done!
– Pspl
Aug 19, 2020 at 12:41
• @Pspl was still pretty tricky!! The hardest part was definitely working out the order Aug 19, 2020 at 12:43
• @Pspl done! I kept getting June and July confused :P Aug 19, 2020 at 12:58