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Problem of the Week

Problem B and Solution

Word Up!


In the diagram below, we can connect the letters of the word PLAY by drawing a straight line between each pair of consecutive letters in the word, and then another straight line from the last letter back to the first.
When we connect the letters of the word PLAY, we can see that the shape formed is a rectangle.

A four by four grid with each cell containing a letter. Row 1 is S, H, P, K. Row 2 is Y, E, B, G. Row 3 is U, O, D, L. Row 4 is I, A, M, C. A rectangle is drawn on the grid with vertices at the letters P, L, A, and Y.

  1. Which of the words shown below will also create a rectangle when we connect their letters in the given diagram?


  2. Name the shapes formed when we connect the letters of these words:

Challenge: What other words can you find which make polygons when you connect their letters in the given diagram?


  1. SICK, SULK, HACK and PLAY form rectangles.
    Note that SICK and PLAY form squares, but as a square is a type of rectangle, we include these.
    Note also that though a square is a rectangle, a rectangle is not always a square.

  2. The shapes formed are:

    BEAM: rectangle
    BOYS: quadrilateral
    DAM: isosceles right-angled triangle

Challenge: Various words and polygons are possible, including:
YOU: isosceles right-angled triangle
MOB: isosceles right-angled triangle
BAM: right-angled triangle
POD: right-angled triangle
CASH: quadrilateral
MASH: parallelogram
POSH: isosceles triangle
GOAL: parallelogram