Ten little circles are drawn on a squared board \(4\times4\).
Cut the board into identical parts in such a way that each part contains 1, 2, 3, and 4 drawn circles correspondingly.
Philip and Denis cut a watermelon into four parts. When they finished eating watermelon (they ate the whole thing), they discovered that there were five watermelon rinds left. How is it possible, if no rind was cut after the initial cutting?
Cut a square into a heptagon (7 sides) and an octagon (8 sides) in such a way, that for every side of an octagon there exists an equal side belonging to the heptagon.
Cut a rectangle into two identical pentagons.
(a) Cut the rectangle into two identical quadrilaterals.
(b) Cut the rectangle into two identical hexagons.
(c) Cut the rectangle into two identical heptagons.
a) You have a \(10\times20\) chocolate bar and 19 friends. Since you are good at maths they ask you to split this bar into 19 pieces (always breaking along the lines between squares). All the pieces have to be of a rectangular shape. Your friends don’t really care how much they will get, they just want to be special, so you need to split the bar in such way that no two pieces are the same.
(b) The friends are quite impressed by your problem solving skills. But one of them is not that happy with the fact you didn’t get a single piece of the chocolate bar. He thinks you might feel that you are too special, therefore he convinces the others that you should get another \(10\times20\) chocolate bar and now split it into 20 different pieces, all of rectangular shapes (and still you need to break along the lines between squares). Can you do it now?
Can one cut a square into (a) one 30-gon and five pentagons? (b) one 33-gon and three 10-gons?
After having lots of practice with cutting different hexagons with a single cut Jennifer thinks she found a special one. She found a hexagon which cannot be cut into two quadrilaterals. Provide an example of such a hexagon.
Two people had two square cakes. Each person made 2 straight cuts from edge to edge on their cake. After doing this, one person ended up with three pieces, and the other with four. How could this be?
How can you divide a pancake with three straight sections into 4, 5, 6, 7 parts?