John drunk a of a full cup of black coffee and then filled the cup back up with milk. Then he drunk a third of what he had in the cup. Then, he refilled it back to full with milk again, and after that, drunk a half of the cup. Finally, he once again refilled the cup with milk and drunk everything he had. What did he drink more of - coffee or milk?
A round necklace contains beads of two different colours: red and blue. Show that it is possible to find two beads of the same colour next to each other.
A square has been divided into rectangles and a square. If the rectangle in the bottom left corner has dimensions and the one in the top right is , what is the area of the small square in the middle?
There are bugs sitting on the squares of a board, at each square. When I clap my hands, each bug jumps to a square diagonally from where it was before. Show that after I clap my hands, at least squares will be empty.
Replace all stars with ”+” or ”” signs so the equation holds: Extra brackets may be added if necessary. Please write down the expression into the answer box.