2024-10-12 08:00:00
Major reforestation plans have been initiated on the deserted Bachmakov Plains. Mainly two types of trees, birches and firs, are planted here, but forestry engineers have established some rules regarding their distribution. Exactly one kilometer from every fir tree in the forest we must always find the same number of birch trees. And, exactly one kilometer from each birch, we must also find the same number of fir trees.
The following figure shows a category 2 forest, i.e. for which the number in question is equal to 2. At this stage the word “forest” is certainly a bit exaggerated, since it is not made up of just four trees arranged in diamond shape whose side measures one kilometer. In fact, you can observe that, in this way, there are exactly two fir trees one kilometer from each birch tree and two birch trees one kilometer from each fir tree. Bachmakov’s engineers initially thought of covering the plains with a multitude of small diamonds to form a vast category 2 forest. But the result was considered too small and it was decided to examine the possibility of designing higher category forests.
Following the same rules, in a category 3 forest, each birch tree is located exactly one kilometer from three fir trees, and each fir tree is located exactly one kilometer from three birch trees. And, of course, it is impossible to plant two trees in the same place.
Can you represent the arrangement of trees in a category 3 forest?
Can you imagine a method for designing a category 4, or 5, or higher Bachmakov forest? At least how many trees will be needed to plant to design a category 10 forest?
Find previous puzzles by clicking here
#Bachmakovs #forest #mathematical #enigma #World