Bored? Try this math challenge. :)

Suppose there are two points, • •, when you draw a line between them they make one pair, •---•.

With three points you can draw lines to make three pairs:


Define the relationship between the number of points x and the maximum number of pairs you can draw between them y.


Have fun!

I'll just leave this here before going to sleep:

Oh, you sneaky devil. That one wasn't really hard but it took a surprisingly long time before I got it. Too long, really.

It's a combination. You can rewrite that problem as "How many ways do you have to take two elements (pair) from a set (of points) if order doesn't matter", and the answer would be:

x!/[(x-2)!2!]=x(x-1)/2

Right, but the purpose of the problem isn't to study combination mathematics in general but to show a fairly easy and interesting problem to help someone teach themselves how a relationship can arise into an equation that they hopefully would be able to define completely by themselves, which is also why I phrased the solution the way I did.

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GeorgAnatoly wrote:

Right, but the purpose of the problem isn't to study combination mathematics in general but to show a fairly easy and interesting problem to help someone teach themselves how a relationship can arise into an equation that they hopefully would be able to define completely by themselves, which is also why I phrased the solution the way I did.

Your definition was very crude and ambiguous. Perhaps next time you should define the problem more clearly.

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GeorgAnatoly wrote:

There are two points and you can draw a line between them making one pair. With three points you can draw lines to make three distinct pairs.

You should have fully and explicitly stated what you meant by 'making one pair'. A pair of what?

The answer is obviously square.

Peace,

-Boem-

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SkyCore wrote:

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GeorgAnatoly wrote:

Right, but the purpose of the problem isn't to study combination mathematics in general but to show a fairly easy and interesting problem to help someone teach themselves how a relationship can arise into an equation that they hopefully would be able to define completely by themselves, which is also why I phrased the solution the way I did.

Your definition was very crude and ambiguous. Perhaps next time you should define the problem more clearly.

"

GeorgAnatoly wrote:

There are two points and you can draw a line between them making one pair. With three points you can draw lines to make three distinct pairs.

You should have fully and explicitly stated what you meant by 'making one pair'. A pair of what?

Thanks for the feedback, I want to make myself as clear as possible.

I first became interested in that type of function as a young man due to my interest in... Warcraft 2.

Let's say I set up a choke point such that only one enemy unit can attack my units, but all of mine can attack that one. How many enemy units y could be defeated one-at-a-time, assuming I had x identical units?

Obviously if x=1 then y=1.

If x=2, then let's say units deal 1 damage and have 2 HP, so the first two enemy units kill just one guy, and the next one kills my other guy. If x=2 then y=3.

For x=3, let's give units 1 damage and 6 health. The first three enemy units deal 2 damage each before dying, taking out one defender. The next two deal 3 before dying and take out the second defender. The last takes out the final defender.

So the choke point advantage formula is equal to x*(x+1)/2, where x is the ratio between choke point defenders and the size, in combat units, of the choke point.

I went through it twice and have two possible solutions:
1. Bananas, because black holes can't do marathon runs in russian divided by 0
2. 42
Not sure which one though...