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You are given a series of 10 geometric computer tasks labeled R0, …, R9; to open the tasks, use the links at the bottom of this the page. In each task, you will find a 6×6 grid, and you will have to construct one or several rhombi with vertices on the grid nodes. Your constructions are to be performed with the tools on the toolbar left of the grid; the main tools are Line and Polygon.

R0 is an easy exercise that must help you to get used to the tools.

In R1 and R2, one has to construct as many rhombi satisfying the given conditions as possible.

In tasks R3–R9 you have not only to construct a rhombus described in the statement, but to do this in the shortest possible way, that is, using as few auxiliary lines as you can. Of two constructions with the same number of auxiliary lines, the one with a smaller number of new points is valued more. You can (and should) use the grid lines and nodes in your constructions; they are not counted in the assessment of

After pressing the Check your answer button (it is blue) below the grid, you’ll be told whether your construction is correct and how many auxiliary figures you have created. Improving your solution, you can use this button as many times as you want. The green button Submit your answer sends your results to the server to be registered and checked. If you press it by mistake or find a better solution, you can submit updated answers only two more times—three attempts altogether! (This button was operating only during the competition.)

R0 R1 R2 R3 R4 R5 R6 R7 R8 R9

Warning: the first task you’ll open may take a relatively long time to load. Subsequent tasks will open faster.
Before you start, please read carefully the short User Guide.
We owe the idea of this contest as well as most of the questions to the authors of Pythagorea, a geometric computer game, to whom we are sincerely grateful. The tasks are implemented in 1C:MathKit 8 environment.

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