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Problems
1Vid cut a square \(ABCD\) of side length \(20\) units into \(400\) unit squares. Eva then picked four vertices of unit squares, all lying in the interior of \(ABCD\), that are the vertices of a rectangle …Open2At a national competition the students worked on \(4\) problems. Each problem was marked with a whole number of points, at least \(0\) and at most \(7\). Altogether \(42\) students competed. Exactly half …3Borut drew the table of size \(2 \times 7\) shown in the picture. He now wants to colour some of its cells so that every cell he leaves uncoloured shares a side with at least one coloured cell. What is …4Peter keeps \(111\) red and \(111\) blue marbles at home; they are made by his uncle. Every day Peter may visit his uncle and carry out one exchange: either he hands over \(11\) red marbles and receives …5Jure drew four distinct lines in the plane, one arrangement after another, and for each arrangement he wrote down the number \(n\) of points at which at least two of his lines cross. Which of the sets …6Lara and Sara draw \(n\) straight lines on a rectangular sheet of paper, taking turns and drawing one line each time. Every line is parallel to one of the edges of the sheet and runs from edge to edge, …
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