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Problem of the Week
Problem B
Sorting Marbles

Dr. Cy Linder has tubes containing marbles of different colours which he would like to sort. He pours marbles from one tube to another until all the marbles of the same colour are in their own tube. For example, Dr. Linder starts with blue and red marbles in the three tubes shown.

Tube 1 contains 3 stacked marbles; the top and middle marbles are blue and the bottom marble is red. Tube 2 contains 2 stacked marbles; the top marble is red and the bottom marble is blue. Tube 3 is empty.

He can sort the marbles by first pouring both blue marbles from Tube 1 to Tube 3. Next he pours the red marble from Tube 2 to Tube 1. Finally he pours the blue marble from Tube 2 to Tube 3. The marbles are now sorted, and it took 3 pours in total. Note that this is not the only way to sort these marbles.

A description of the diagram follows.

  1. Write down steps to sort the marbles in the given tubes. How many pours did you need in total?

    Three tubes. Tube 1 contains 4 marbles: from top to bottom, the colours are red, blue, red, blue. Tube 2 contains 4 marbles: from top to bottom the colours are blue, red, blue, red. Tube 3 is empty.

  2. Write down steps to sort the marbles in the given tubes. How many pours did you need in total?

    Five tubes. Tube 1 contains 4 marbles: from top to bottom they are blue, red, grey, blue. Tube 2 contains 4 marbles: from top to bottom they are blue, red, grey, grey. Tube 3 contains 4 marbles: from top to bottom they are grey, red, blue, red. Tubes 4 and 5 are empty.

Extension: Create your own marble sorting problem that requires 5 pours to be sorted.

Theme: Computational Thinking