It is easy to construct one equilateral triangle from three identical matches. Can we make four equilateral triangles by adding just three more matches identical to the original ones?
Does there exist a quadrilateral which can be cut into six parts with two straight lines?
A square \(4 \times 4\) is called magic if all the numbers from 1 to 16 can be written into its cells in such a way that the sums of numbers in columns, rows and two diagonals are equal to each other. Sixth-grader Edwin began to make a magic square and written the number 1 in certain cell. His younger brother Theo decided to help him and put the numbers \(2\) and \(3\) in the cells adjacent to the number \(1\). Is it possible for Edwin to finish the magic square after such help?
Cut a square into \(3\) parts which you can use to construct a triangle with angles less than \(90^{\circ}\) and three different sides.
A chord of a circle is a straight line between two points on the circumference of the circle. Is it possible to draw five chords on a circle in such a way that there is a pentagon and two quadrilaterals among the parts into which these chords divide the circle?
Is it possible to cut an equilateral triangle into three equal hexagons?