Puzzles
20 December
![](javascript:showlimage("advent2022-20corrected.png"))
The diagram to the right shows (two copies of) quadrilateral ABCD.
The sum of the angles ABC and BCD (green and blue in quadrilateral on the left) is 180°.
The sum of the angles ABC and DAB (green and orange in quadrilateral on the left) is also 180°.
In the diagram on the right, a point inside the quadrilateral has been used to draw two triangles.
The area of the quadrilateral is 850. What is the smallest that the total area of the two triangles
could be?
12 December
![](javascript:showlimage("advent2020quads.png"))
The diagram to the left shows a large black square. Inside this square, two red squares have been drawn.
(The sides of the red squares are parallel to the sides of the black square; each red square shares a vertex with the black square; and the two red squares share a vertex.)
A blue quadrilateral has then been drawn with vertices at two corners of the black square and the centres of the red squares.
The area of the blue quadrilateral is 167. What is the area of the black square?