Personal Comment: This is not as hard as it looks. Just figure out what the trick is and you are set!

Birds and the Trees Enigma

What we know: There is this forest with trees. On each and every tree in the forest, exactly the same number of birds are sitting on it (ex. "There are 5 trees and each tree has 5 birds on it"). The birds in the forest is a given number between 200 and 300

Enigma: How many trees are in our forest(such that there is no other combination of trees and birds to acquire the same product)?

Solution: If T is the number of trees and B is the number of birds per tree, then the total number of birds in the forest is product T*B, which is between 200 and 300. If the numbers T and B were not equal then there wouldn't be one UNIQUE solution (because the T and B could swap). Lets take T=16 and B=15 which looks like a good answer. The product 15*16 = 240 and it is between 200 and 300. So the answers are: a. for 240 birds there can be 15 trees (if we have 16 birds per tree) b. for 240 birds there can be 16 trees (if we have 15 birds per tree) This is not a UNIQUE answer! Generalizing this espial, T and B MUST be equal. Thus we are looking for a number whose square is between 200 and 300. The candidates are 15, 16 and 17. It can't be 15, because 15*15 = 45*5 = 5*45, so again NO unique answer on the number of trees. Similarly it can't be 16, because 16*16 = 8*32 = 32*8. But 17*17 = 289 and there isn't any other pair of numbers whose product is 289. So, for 289 birds there can be only 17 trees in the forest (with 17 birds per tree) and this is the only unique answer available.

See who got this right

Previous Enigma | Enigma Index | Next Enigma

This window to the Fourth Dimension is hosted by Geocities