CEMC Banner

Problem of the Week
Problem A
Picture Pixels

Akhil sends codes to his friends that tell them how to shade in squares of a grid to reveal a secret picture. Each code contains a blank grid with a list of numbers next to each row, which are used to shade in the row from left to right. The first number in a list represents the number of blank squares at the beginning of the row. The second number represents the number of squares that need to be shaded next. After that, the numbers alternate between the number of blank squares and the number of shaded squares until you reach the end of the row.

For example, if the list of numbers was \(2\), \(2\), \(1\), then the leftmost \(2\) squares would be blank, the next \(2\) squares would be shaded, and the next square would be blank. A completed picture is shown.

A grid with 3 rows and 5 columns. The first row has list 2, 2, 1 and, from left to right, has 2 blank squares, then 2 shaded squares, then 1 blank square. The second row has list 1, 3, 1 and, from left to right, has 1 blank square, then 3 shaded squares, then 1 blank square. The third row has list 0, 2, 1, 2 and, from left to right, has two shaded squares, then one blank square, then two shaded squares.

  1. Draw the picture for the given code.

    A description of the code follows.


  2. Akhil turns some of his codes into puzzles. For each column, he adds a list of numbers representing the number of blank and shaded squares, as he has for the rows. Then, for each row and column, he removes the numbers representing blank squares. Two of his puzzles are shown. Try to solve them.


    1. A description of the puzzle follows.




    2. A description of the puzzle follows.


Theme: Computational Thinking