Funny riddle, here's how I figured it:
The way it seems to happen is using them both in perpendicular way in one of the corners of the ditch, making a diagonal. Like the image below:
So, easy pictured, but how to reach this point?
In order to not walk into wrong paths and simply ending up trapped forever, some previous calculations are needed. How far and how close must the edges of the first log can be, in order to establish that connection? First of all I will identify the sizes in need of measuring. They are:
- Whites have the same measure;
- Orange is half of Yellow;
The key here are the whites. Establishing the limits, I started by the smaller limit.
So, as we know, that square is 3m x 3m. That makes diagonal measuring √18 (I will use exact values until the end, in order to achieve exact results, and not rounded up). Green must be bigger than √(18) - 3. Having these calculations, trigonometry gets in action and White is 6-3√2, or 1,76. This is the smaller limit: 1,76.
After it, let's get to the bigger limit.
The bigger limit can be achieved when we assume that Yellow cannot be bigger or equal than 3 meters. Otherwise, he would fall. Pythagoras comes in again and turns this into 32= x2+x2, and x = 3/√2, or 2,12.
So, finally, we have them limits, 1,76 < White < 2,12. It means it can be chosen any size between these two values. Surprise surprise, let's choose 2.
Still, there is one last question: How to find the half of the log? And, moreover, how to measure 2 meters?
Well, I guess that I don't have any mathematical answer to that. Instead, if you put the two logs side by side, and slide one of them until they become three equal parts of 1,5 meters. Pick up a small stone (there must be some left), and mark the first log you will need. And how about 2 meters? Do as the image says:
Mark the second log, put it on the White lines, and he has the measures. Unless he is cross-eyed, he shall mark it correctly, and still can miss it by some centimeters. Set them up, and he is free to leave.