horses and corrals

Question

Place 27 horses in  4 corrals  so that each Corral contains an odd number of horses 

Answer 1

There's a way. Some teacher is out there laughing at us. Or at me, anyway. LOL

 

Take the four corrals. With each one, make the fourth side diagonal. Gonna be hard to represent this here. But I will try.

 

+==========+==========+

| 1                      |                     2 |

|                         |                        |

|                    +===+                   |
|                   /           \                  |

|                 /               \                |

+======/       open     \======+

+======\       area     /======+
|                \                /                |
|                  \            /                  |

|                    +===+                   |
|                         |                        |
| 3                      |                     4 |

+==========+==========+

 

There you go. Stick a horse in that open area bordered by the four actual corrals. Then you can put an odd number of horses in each of the others. The open area is not a corral itself per se: just bordered by the others. You may say it's a corral if you give it a gate of its own. LOL

 

Yeah, I know it's a cheat. But we're arguing the whole question is a cheat. LOL

*********

 

And THEN...

 

I was talking to some friends about this problem, and one of my friends shamed me.

 

Make three corrals, divide up the horses into three odd numbers (9, 9, 9?), then make a fourth corral *around the first three*. All 27 are then in the fourth. Duh. LOL

 

Answer 2

It's a word problem with lots of grammatical mistakes.

Answer 3

"each Corral contains an odd number of horses" places a big restriction on what can be done.

 

That's because:

    -   when any two even numbers are added, the sum is an even number

    -   when any two odd numbers are added, the sum is an even number

 

For the sum of adding two numbers together to be odd, exactly one of the numbers must be odd.

 

What about four (corrals)?  Well, that two corrals plus two corrals.

 

The number 27 is odd, so the only ways to have four corrals of horses add up to 27 (an odd number), is to have one of these situations:

    E E  E O         (E=even; O=odd)

    E E  O E

    E O  E E

    O E  E E

    E O  O O

    O E  O O

    O O  E O

    O O  O E

 

Sorry, none of those are "O O  O O."