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Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.

  • A.Three flat pieces: a pentagon-like piece with a round notch on its right edge, an angular piece with a small clipped corner, and a large piece with a V cut and a round notch on top
  • B.Three flat pieces: a tall piece with a small stepped round notch, a large piece with a V cut and a round notch on top, and a slanted quadrilateral with a round notch on the left
  • C.Three flat pieces: a tall piece with a stepped round notch, an angular piece with a round notch on its lower left, and a large piece with a V cut and a round notch on top
  • D.Three flat pieces with straight edges only and no curved notches: a tall piece with a stepped side, an angular piece, and a large piece with a V cut

Answer: C

The set that works is (C).

In each set, two pieces carry square corners at the top (the left piece the top-left corner, the middle piece the top-right corner) and the large piece has a flat bottom and two square lower corners, so together they can make a square. The pointed lower end of the left piece fits the V-shaped notch in the top edge of the large piece, and the peak of the large piece fits under the inverted V of the middle piece.

The hole comes from curved notches. In (C) each of the three pieces has a curved notch on an inner edge, and when the pieces are fitted together the three notches meet near the centre to close one round hole.

(D) has no curved notch on any piece, so it cannot leave a round hole. In (A) the middle piece has no notch, and the notch on the large piece is cut beside its peak rather than at the inner corner, so the curved edges do not come together as one circle. In (B) the third piece is a four-sided piece with no inverted V, so it cannot fit over the peak of the large piece and the pieces do not form a square.

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