must there be at least two trees with the same number of leaves if no tree can have zero leaves?
2006-06-23 05:58:25 · 5 answers · asked by Finnegan 7 in Games & Recreation ➔ Other - Games & Recreation
The question is (again, due to misunderstanding the first time), if there are more trees in the world than leaves on any one tree, must there be at least two trees with the same number of leaves if no tree can have zero leaves.
2006-06-23 06:43:06 · update #1
I think I understand the question, and the answer is most definately yes.
If there are X number of trees, and all those trees have less than X leaves, than at least two trees must have an equal number of leaves.
Let's say there are 5 trees in the world, and each has 1, 2, 3, or 4 leaves.
Then
T1 has 1 leaf
T2 has 2 leaves
T3 has 3 leaves
T4 has 4 leaves
This is the most distributed the values can be. So now what does T5 have? No matter how many leaves it has, it must match at least one other tree. The proof is the same for billions of trees, but it takes a little longer to type out.
2006-06-23 08:14:50 · answer #1 · answered by Mantis 6 · 2⤊ 1⤋
yes of course there are more trees than leaves on any one tree.
2006-06-23 13:03:26 · answer #2 · answered by Tom B 1 · 0⤊ 0⤋
some have zero...they are called pine trees
2006-06-23 13:01:49 · answer #3 · answered by JeNe 4 · 0⤊ 0⤋
thats true. it was told by German mathematician Gauss to his father when they were walking in the forest, he was just 6 years old.
2013-12-23 14:23:43 · answer #4 · answered by hakan Turk 2 · 0⤊ 0⤋
How you thought that up is beyond me, but yes.
2006-06-23 18:56:18 · answer #5 · answered by pseudonym 5 · 0⤊ 0⤋