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John drunk a 16 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 45 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.

Cut this figure into 4 identical shapes. (Note: you have to use the entire shape. Rotations and reflections count as identical shapes)

The diagram shows a 3×3 square with one corner removed. Cut it into three pieces, not necessarily identical, which can be reassembled to make a square:

Find all possible non-zero digits A for which the following holds (AA+AA+1)×A=AAA. (Recall AA means the two-digit number whose first and second digits are A)

A square has been divided into 4 rectangles and a square. If the rectangle in the bottom left corner has dimensions 1×4 and the one in the top right is 2×5, what is the area of the small square in the middle?

There are 25 bugs sitting on the squares of a 5×5 board, 1 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 5 squares will be empty.

In a convex quadrilateral ABCD, all the triangles ABC, BCD, CDA and DAB have equal perimeters. Show that ABCD is a rectangle.

Find the last two digits of the number 333333333333333333474111111111111111111474

Replace all stars with ”+” or ”×” signs so the equation holds: 123456=100 Extra brackets may be added if necessary. Please write down the expression into the answer box.