MathDB

11

Part of 2016 ASDAN Math Tournament

Problems(2)

2016 Guts #11

Source:

8/14/2022
Ebeneezer is painting the edges of a cube. He wants to paint the edges so that the colored edges form a loop that does not intersect itself. For example, the loop should not look like a “figure eight” shape. If two colorings are considered equivalent if there is a rotation of the cubes so that the colored edges are the same, what is the number of possible edge colorings?
2016Guts Round
2016 Team #11

Source:

8/17/2022
Let ABCABC be a triangle with AB=2AB=2, BC=3BC=3, and AC=4AC=4. Consider all lines XYXY such that XX lies on ACAC, YY lies on BCBC, and △XYC\triangle XYC has area equal to half that of △ABC\triangle ABC. What is the minimum possible length of XYXY?
2016team test