It will be seen from the diagram how a square piece of flooring may be paved with sixty-two square tiles of the eight colours violet, red, yellow, green, orange, purple, white, and blue (indicated by the initial letters), so that no tile is in line with a similarly coloured tile, vertically, horizontally, or diagonally.  Sixty-four such tiles could not possibly be placed under these conditions, but the two shaded squares happen to be occupied by iron ventilators.

[Illustration: 

+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| V | R | Y | G | O | P | W | B |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| W | B | O | P | Y | G | V | R |
+—–­+—–­*===*—–­+—–­*===*—–­+—–­+
| G | P H W H V | B H R H Y | O |
+—–­+—–­*===*—–­+—–­*===*—–­+—–­+
| R | Y | B | O | G | V | P | W |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| B | G | R | Y | P | W | O | V |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| O | V | P | W | R | Y | B | G |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| P | W | G | B | V | O | R | Y |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|///| O | V | R | W | B | G |///|
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+

]

The puzzle is this.  These two ventilators have to be removed to the positions indicated by the darkly bordered tiles, and two tiles placed in those bottom corner squares.  Can you readjust the thirty-two tiles so that no two of the same colour shall still be in line?

303.—­UNDER THE VEIL.

[Illustration: 

+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   | V | E | I | L |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   | I | L | V | E |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| I | V |   |   |   |   | L | E |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| L | E |   |   |   |   | I | V |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| V | I |   |   |   |   | E | L |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
| E | L |   |   |   |   | V | I |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   | E | V | L | I |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+
|   |   | L | I | E | V |   |   |
+—–­+—–­+—–­+—–­+—–­+—–­+—–­+—–­+

]

If the reader will examine the above diagram, he will see that I have so placed eight V’s, eight E’s, eight I’s, and eight L’s in the diagram that no letter is in line with a similar one horizontally, vertically, or diagonally.  Thus, no V is in line with another V, no E with another E, and so on.  There are a great many different ways of arranging the letters under this condition.  The puzzle is to find an arrangement that produces the greatest possible number of four-letter words, reading upwards and downwards, backwards and forwards, or diagonally.  All repetitions count as different words, and the five variations that may be used are:  VEIL, VILE, LEVI, LIVE, and EVIL.

This will be made perfectly clear when I say that the above arrangement scores eight, because the top and bottom row both give VEIL; the second and seventh columns both give VEIL; and the two diagonals, starting from the L in the 5th row and E in the 8th row, both give LIVE and EVIL.  There are therefore eight different readings of the words in all.