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An economical car consumes 4.5 kilograms of gasoline (CX8HX18) over a distance of 100 kilometers. How much carbon dioxide (COX2) is emitted over this distance?
Note: Assume that the fuel is completely burned into carbon dioxide and water vapor.
by
Markus Michelmann
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Quadrilateral ABCD has the following properties:
- Opposite angles B and D are each 90∘.
- AB and BC have the same length.
- AD+DC=1.
What can be stated about other quadrilaterals that have the same properties as ABCD?
by
Magnus Seidenfaden
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You select a set of N specific points in the 2D plane with integer coordinates such that, for every pair of the N points, the midpoint of the segment connecting them does not have integer coordinates.
What is the greatest possible value of N?
Below is an invalid selection of 3 points (in red), since the midpoint of BC has integer coordinates.
by
Jeremy Galvagni
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The square has side length 12, and the area of the blue region is 12.
What is combined area of the yellow regions?
by
Khang Nguyen Thanh
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The hero (lower right) and devil (upper left) each take turns moving on the grid with the hero going first. Both move as a King piece would on a chessboard. The devil wins if he can move to the same space as the hero. The hero wins if he can avoid the devil forever.
The devil can always win on a 3 x 3 board.
Who will win on an 8 x 8 board?
by
Agnishom Chattopadhyay
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