How many trees.....

Mike Corazzi

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....how many trees have to be in a forest to guarantee that at least two trees have the same number of leaves?
🧐
 

Paradox

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No clue
Go out into a forest and count the leaves on the tree and tell us how many you had to count before you found two with the same number
 

Forsoothe!

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In winter, they all have the same number.
 

Wires_Guy_wires

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As most seedlings start with two leaves and the definition of a forest is blurry, I say five adult trees and two seedlings.
 

Mike Corazzi

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cause you're right.
Let X = the number of leaves on the tree with the most leaves.
Then to guarantee that at least two trees in the forest have the same number of leaves, you need X+1 trees in the forest.

For example, if the tree in a forest with the most leaves has 100K leaves on it, then you need 100001 trees in that forest to ensure that at least two trees have the same number of leaves. Now, you not only don't know how many leaves they have on them, and you have no clue where they are, but you can be damned sure they exist.
 

Forsoothe!

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cause you're right.
Let X = the number of leaves on the tree with the most leaves.
Then to guarantee that at least two trees in the forest have the same number of leaves, you need X+1 trees in the forest.

For example, if the tree in a forest with the most leaves has 100K leaves on it, then you need 100001 trees in that forest to ensure that at least two trees have the same number of leaves. Now, you not only don't know how many leaves they have on them, and you have no clue where they are, but you can be damned sure they exist.
I hope you don't use this same logic to function in life. It's the kind of "if, come" thinking that is used to beat the roulette wheel.
 

Woocash

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I hope you don't use this same logic to function in life. It's the kind of "if, come" thinking that is used to beat the roulette wheel.
No it’s just maths. Beating a roulette wheel uses probabilities, this little problem uses absolutes.
 

Woocash

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If you know which tree has the most leaves (tree x) and you have a forest with the same number of trees as there are leaves on that tree, then either all the trees have an increasing number of leaves from 1,2,3 etc all the way up to the number of leaves on tree x, or there is at least one pair with a duplicate number of leaves. We add one extra tree in the event that only tree x is duplicated You can’t have more leaves than tree x because that tree has the highest amount in the forest.

Obviously, it is all theoretical. You would be very hard pushed to prove it physically, but the maths can not be argued with.
 

Woocash

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Please show your math.
If you know which tree has the most leaves (tree x) and you have a forest with the same number of trees as there are leaves on that tree, then either all the trees have an increasing number of leaves from 1,2,3 etc all the way up to the number of leaves on tree x, or there is at least one pair with a duplicate number of leaves. We add one extra tree in the event that only tree x is duplicated You can’t have more leaves than tree x because that tree has the highest amount in the forest.

Obviously, it is all theoretical. You would be very hard pushed to prove it physically, but the maths can not be argued with.
 

Forsoothe!

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Forgive me, but that is the lamest imitation of a mathematical explanation I have ever heard. You are postulating assumptions if come assumptions with an unlimited set of variables, and without a single known factor. "Very hard pushed to prove," indeed.
 
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