Informational Site Network
 Privacy

 Home Top Rated Puzzles Most Viewed Puzzles All Puzzle Questions Random Puzzle Question Search

## THE EIGHT VILLAS.

(Combination and Group Problems)
In one of the outlying suburbs of London a man had a square plot of
ground on which he decided to build eight villas, as shown in the
illustration, with a common recreation ground in the middle. After the
houses were completed, and all or some of them let, he discovered that
the number of occupants in the three houses forming a side of the square
was in every case nine. He did not state how the occupants were
distributed, but I have shown by the numbers on the sides of the houses
one way in which it might have happened. The puzzle is to discover the
total number of ways in which all or any of the houses might be
occupied, so that there should be nine persons on each side. In order
that there may be no misunderstanding, I will explain that although B is
what we call a reflection of A, these would count as two different
arrangements, while C, if it is turned round, will give four
arrangements; and if turned round in front of a mirror, four other
arrangements. All eight must be counted.
[Illustration:
/ / /
|2 | |5 | |2 |
/ /
|5 | |5 |
/ / /
|2 | |5 | |2 |
+---+---+---+ +---+---+---+ +---+---+---+
| 1 | 6 | 2 | | 2 | 6 | 1 | | 1 | 6 | 2 |
+---+---+---+ +---+---+---+ +---+---+---+
| 6 | | 6 | | 6 | | 6 | | 4 | | 4 |
+---+---+---+ +---+---+---+ +---+---+---+
| 2 | 6 | 1 | | 1 | 6 | 2 | | 4 | 2 | 3 |
+---+---+---+ +---+---+---+ +---+---+---+
A B C
]

Next: COUNTER CROSSES.

Previous: THE SIXTEEN SHEEP.

### Random Questions

Crossing The Stream.
Measuring, Weight, and Packing Puzzles.
The Square Of Veneer.
Various Dissection Puzzles
The Miners' Holiday.
Money Puzzles
Magic Squares Of Two Degrees.
Magic Squares Problem.
The Motor-car Tour.
Unicursal and Route Problems
The Two Trains.
Money Puzzles
Youthful Precocity.
Money Puzzles
Ancient Chinese Puzzle.
The Guarded Chessboard
The Nine Schoolboys.
Combination and Group Problems
Changing Places.
Money Puzzles
The Wizard's Arithmetic
MISCELLANEOUS PUZZLES
Mrs. Perkins's Quilt.
Patchwork Puzzles
The Landowner's Fences.
Various Dissection Puzzles
Two New Magic Squares.
Magic Squares Problem.
A Puzzle For Motorists.
Unicursal and Route Problems