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Problem of the Week
Problem B
Playing with Bricks

Saskia has the following five sizes of LegoTM bricks.

A 2 times 2 brick with width 2 and length 2. A 2 times 3 brick with width 2 and length 3. 2 times 4 brick with width 2 and length 4.

A 2 times 8 brick with width 2 and length 8. 2 times 10 brick with width 2 and length 10.

For each question below, assume that Saskia will never run out of bricks.

  1. Saskia wants to make a row of bricks that measures \(2 \times 16.\) Which of her brick sizes can she use if all bricks used must be the same size?

  2. Saskia wants to make a rectangular frame of bricks that measures \(14 \times 20\) on the outside, as shown. Which of her brick sizes can she use if all bricks used must be the same size?

    A frame with outer dimensions of 14 by 20. The frame border has a width of 2.

  3. Saskia wants to make a rectangular frame of bricks that measures \(320 \times 420\) on the outside. What is the largest brick size that she can use if all bricks used must be the same size?