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Problem of the Week
Problem C
Crossing Canals

Koji is rowing his boat on a busy canal system near his home. The following diagram shows the canal system with a star representing Koji’s current location and the house representing the location of his home.

A grid of squares with 7 horizontal rows and 9 vertical
    columns. All of the squares in the second and fifth rows are coloured
    blue. All of the squares in the second, fifth, and eighth columns are
    coloured blue. These blue rows and columns intersect at six different
    squares. The star is in the fifth column, placed on the top edge of the
    bottom square. The house is in the second column, placed on the top edge
    of the fourth square from the bottom.

From Koji’s extensive canal experience, he knows the following:

  1. Rowing straight across an intersection square takes \(30\) seconds.

    A row of three squares intersects a column of
  three squares forming a plus sign. A straight arrow points from the left
  edge of the middle square to the right edge.

  2. Rowing straight across a square that is not an intersection takes \(20\) seconds.

    A row of three squares. A straight arrow points from the
    left edge of the middle square to the right edge.

  3. Turning right at an intersection takes \(15\) seconds.

    A row of three squares intersects a column of three squares
    forming a plus sign. A bent arrow points from the bottom edge of the
    middle square to the right edge.

  4. Turning left at an intersection takes \(270\) seconds, due to heavy traffic.

    A row of three squares intersects a column of three squares
    forming a plus sign. A bent arrow points from the bottom edge of the
    middle square to the left edge.

  5. It is not possible make U-turns or reverse direction.

Calculate the shortest amount of time it will take Koji to row home from his current position, using only the canals shown.

Not printing this page? You can use our interactive worksheet.

This problem was inspired by a past Beaver Computing Challenge (BCC) problem.


Theme: Computational Thinking