Birds and Trees


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

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There are 289 birds and 17 trees in the forest (with 17 birds per tree).

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.


dasari said...

The number of trees and birds together is 289...i.e 17*17..

Jayant said...

First, I think that the question is very ambiguously framed...
And to add to it, the constraint given in the brackets adds to it...
So from the constraint, the number of birds per tree and the number of tree constraint gets kinda confusing...

T: no. of trees
B: no. of birds per tree

So, first take...
1. T != B
Then clearly we have
i. T and B are prime numbers.
ii. 200< T*B < 300
for example, (T,B) = (11,23),(13,17) etc

2. T == B (this is what one would interpret the question, but the constraint in the bracket kinda confuses )
Then clearly, its just another constraint added to the first scenario, i.e.
and iii. T == B
So, T = B = 17.

pg... said...

Answer is 17 trees.

The perfect squared terms between 200, 300 are 15,16,17 .

15*15 =3*75=75*3= 45*5 = 5*45, number of trees are not unique.
Similarly answer is not 16, because 16*16 =4*64=64*4= 32*8 = 8*32.(not unique number of trees)
But 17*17 = 289 ,
the factors for 289 only 17. 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.

Novice Academician said...

Well, the hint says for 5 trees, there will be 5 birds on each tree. so total number of birds will be 5*5*5=125. since total number of birds is a given number between 200 and 300, the combination of trees and birds should be 6*6*6, ie., there are 6 trees, 6 birds in each of the trees. this is the only combination which will give total number of birds within 200 and 300.

incorrigiblix said...

ya 17 * 17 is rite!!

Novice Academician said...

oops, I understood the puzzle wrongly :(

v fcv said...


Hemant said...

Puzzle is very good. Nice collection.
for more pls check

Atul said...

Puzzles pls read.