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If y2−4y=x2−4x, then does it necessarily follow that y=x?
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How many ways are there to paint a 3×3 grid with three colors such that each row and column has all three distinct colors?
Note: If you rotate the above illustration by 90∘,180∘ or 270∘, they each count as different ways to paint the 3×3.
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In the diagram below, ABGF is a trapezoid and D is the intersection point of its diagonals.
If CE is drawn such that it passes through D and is parallel to AB, is it true that CD=DE?
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In a small, remote country, there are only two types of bills--the $X bill and the $Y bill.
With combinations of these bills, almost all positive integer prices can be paid exactly. Only fifteen positive integer prices can't be paid exactly, one of which is $18.
What is X+Y?
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All the resistors in the above circuit have equal resistance R=10 Ω. Calculate the equivalent resistance Re between points A and B in ohms. Submit your answer to the nearest integer.
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