CISRA Puzzle Competition 2007 - Solutions

This is the archive of the 2007 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

C.3 Iconoclast

Intuitive Leap: For each prime number, pixels are turned on or off depending on whether each number in the grid has that prime number as a factor.

The prime factors of each number are:

  • [13], [5x7x13x17], [11x13x17x19], [2x3x13x17x19], [11x17x19], [5x7x17], [].
  • [13x17], [5x7x11x17x19], [3x5x11x19], [2x3x5x7x11x19], [3x5x11x19], [5x7x11x17x19], [17].
  • [11x13x17x19], [3x5x7x11x17x19], [3x5x11x17], [2x3x5x7x11x19], [3x5x11x17], [3x5x7x11x13x17x19], [11x17x19].
  • [3x11x13x17x19], [3x7x11x13x17x19], [3x5x7x11x13x17x19], [2x3x7x11x17x19], [3x5x7x11x13x17x19], [3x7x11x17x19], [3x11x13x17x19].
  • [13x17], [11], [2x5x11x19], [2x3x7x17], [5x11x13x19], [11x13], [13x17].
  • [13x17], [2x3x19], [2x5x17], [2x3x5x7x17], [5x13x17], [19], [17].
  • [13], [5x17], [2x3x5x17x19], [5x7x17], [5x17x19], [5x11x13x17], [13].

Using each prime factor in turn, we can make a picture by turning a pixel on in each grid position, if the number in that grid position is a multiple of that prime factor. Eight pictures can be formed this way: 

  2:         3:         5:         7:
+-------+  +-------+  +-------+  +-------+
|   *   |  |   *   |  | *   * |  | *   * |
|   *   |  |  ***  |  | ***** |  | * * * |
|   *   |  | ***** |  | ***** |  | * * * |
|   *   |  |*******|  |  * *  |  | ***** |
|  **   |  |   *   |  |  * *  |  |   *   |
| ***   |  | * *   |  |  ***  |  |   *   |
|  *    |  |  *    |  | ***** |  |   *   |
+-------+  +-------+  +-------+  +-------+
Crotchet   Umbrella   Rook       Trident

 11:        13:        17:        19:
+-------+  +-------+  +-------+  +-------+
|  * *  |  |****   |  | ***** |  |  ***  |
| ***** |  |*      |  |**   **|  | ***** |
|*******|  |*    * |  |*** ***|  |** * **|
|*******|  |*** * *|  |*******|  |*******|
| ** ** |  |*   ***|  |*  *  *|  |  * *  |
|       |  |*   *  |  |* *** *|  | *   * |
|     * |  |*    **|  | ***** |  |  * *  |
+-------+  +-------+  +-------+  +-------+
Australia  Iron       Nuclear    Space invader

The first letters spell CURTAINS, which is the answer.