If \(y^2 -4y = x^2 - 4x,\) then does it necessarily follow that \( y= x?\)
by
Efren Medallo
How many ways are there to paint a \(3\times3\) grid with three colors such that each row and column has all three distinct colors?
Note: If you rotate the above illustration by \(90^\circ, 180^\circ\) or \(270^\circ\), they each count as different ways to paint the \(3\times3\).
by
Geoff Pilling
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 \(CD = DE?\)
by
Worranat Pakornrat
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 \(X+Y?\)
by
Profe Ronald
All the resistors in the above circuit have equal resistance \(R = \SI[per-mode=symbol]{10}{\ohm}\). Calculate the equivalent resistance \(R_e\) between points \(A\) and \(B\) in ohms. Submit your answer to the nearest integer.
by
Djordje Veljkovic