Are you a disciple of the Goddess of wisdom?
Athena, the Olympiad Goddess of wisdom, had a test for her disciples - Odysseus and Perseus. She told them:
I am thinking of a triangle whose sides are integers.
Perseus, I will tell you its perimeter.
Odysseus, I will tell you its area.
You have to figure out the side lengths of the triangle.
Since they were both vying for Athena’s favor, they were hesitant to reveal too much information, and guarded what they said. They made the following statements sequentially:
- Perseus: The Goddess knows that just the perimeter doesn’t tell me the side lengths.
- Odysseus: The Goddess knows that just the area doesn’t tell me what the perimeter is.
- Perseus: Athena be praised, the answer has struck me.
- Odysseus: Athena be praised, the answer has struck me too.
Now, your task is: how many non-congruent triangles could Athena be thinking of?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
“The goddess knows that just the perimeter doesn’t tell me the side lengths.” Therefore, we can immediately eliminate perimeters 3 , 4 , 5 , 6 , 8 as they provide only one possible arrangement for the side lengths(note that different order, e.g. 3 , 4 , 5 ; 3 , 5 , 4 count as the same arrangement.)
-Not Finished-