Mathematical riddles

[Lenin64]

I had a yarn with a mate about this. He was wondering if somewhere out in space there is a colour that we have never seen before and we wouldn't know what it would look like because we have never seen it before,

 

I said that it would still be familair to us and yadda yadda yadda

 

You mean like sort of a Colour Out of Space?

[Guest User]

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[walka92]

These aren't really riddles, but questions I've been wondering.

 

 

 

1. Are there an infinite or finite amount of colors?

 

2. There are an infinite amount of positive numbers. There are also an infinite amount of negative numbers. So, there are an infinite amount of numbers plus another set of infinite numbers when you take the negatives into account. (infinity + infinity) Does this mean something can be over infinity?

there is simply infinte numbers. all you need to know on the matter

[Mr_Adam]

These aren't really riddles, but questions I've been wondering.

 

 

 

1. Are there an infinite or finite amount of colors?

 

2. There are an infinite amount of positive numbers. There are also an infinite amount of negative numbers. So, there are an infinite amount of numbers plus another set of infinite numbers when you take the negatives into account. (infinity + infinity) Does this mean something can be over infinity?

 

 

 

 

 

1) I want to say finite, with the borders being white and black. But then I think of mixing colors together for an infinite amount. But then I think too many colors comes to black. And then I think of spectrums of light not visible #-o

 

 

 

2) Infinity isn't really a number, because there's always something higher. It's just an expression, rather than a variable.

[indy500fan]

1) I want to say finite, with the borders being white and black. But then I think of mixing colors together for an infinite amount. But then I think too many colors comes to black. And then I think of spectrums of light not visible #-o

 

 

 

I already explained about the colours above. A human eye can only see the visible light part of the electro-magnetic spectrum (some people can see a little more on each side, but it isn't much). All colours we see are created by those em-waves. Black isn't a colour, it is a lack of light from the light being absorbed. White isn't a colour, it is all of the different frequencies being reflected back in equal amounts. The colours you don't see on that spectrum picture but that you can see are just a combination of a few of those, along with differing levels of absorption.

[Shinjula]

These aren't really riddles, but questions I've been wondering.

 

 

 

1. Are there an infinite or finite amount of colors?

 

2. There are an infinite amount of positive numbers. There are also an infinite amount of negative numbers. So, there are an infinite amount of numbers plus another set of infinite numbers when you take the negatives into account. (infinity + infinity) Does this mean something can be over infinity?

 

 

 

1.infinite colors; since its subjective what divides two colors we can continually break the spectrum into halves then fourths and so on ad infinitum

 

 

 

2. There are different degrees of infinity; the set of all positive (whole) numbers is small then the set of all positive and negative(whole) number, but both are infinite sets.

 

 

 

Actually while you are quite correct to say that there are different degrees of infinity, the number of positive integers is the same as the number of positive and negative integers (This is something I have studied so I feel confident saying).

 

The proof for this is known as Hilbert's hotel.

 

Imagine a hotel with an infinite number of rooms, guest 1 lives in room 1, guest 2 lives in room two and all the way up to infinity, so the number of rooms is equal to the number of positive integers.

 

Now an infinite number of people arrive at the hotel wanting rooms (the negative numbers , the hotel manager places each person currently occupying a room in the room with the number that is twice the size of his original room number, (so guest 1 is now in room 2, guest 2 is now in room 4 etc) and then fits the new people in the freed up rooms (Guest -1 goes in room 1, guest -2 goes in room 3 and guest -3 goes in room 5)

 

All the guests are still in rooms so the number of positive and negative numbers is equal to the number of room which is equal to the number of positive numbers.

 

 

 

The different sizes of inifinty (called cardinalities) are given different 'Aleph' number, Aleph(0) (spoken as aleph null) is the number of positive whole numbers, the number of positive and negative whole numbers, the number of prime numbers and the number of fractions, these sets are called countably infinite.

 

 

 

Aleph(1) is the number of irrationals which is 'larger' than Aleph(0), irrational numbers are ones which cannot be represented by fractions or repeating decimal expansions, such as the square root of 2, Aleph (1) is also the cardinality of the Transcendental numbers which includes such luminaries as pi and e (Shout me if you want a proof that the irrationals arent countable)

[Harakiri]

 

 

 

Using the above grid, and using all numbers from 1-16, fill it out so that all lines going both across, down and diagonally all add up to the same number:

 

 

 

Simple:

 

 

 

 

 

 

Switch the corner boxes, and flip the middle boxes.

 

 

 

 

 

 

Everything equals 34 when added up.

[brunokiller]

This is a chessboard with two corners cut off.

 

 

 

 

Don't pay too much attention at the fail cropping, I made it quickly lol.

 

 

 

Can you cover it totally with domino stones?

 

 

 

Rules:

 

A domino stone covers a white and a black plane.

 

The domino stones dont atick out/you arent allowed to cut them or something.

[Utopianflame]

brunokiller, no you cant. (# of white squares > # of black squares)

[D Jay99]

brunokiller, no you cant. (# of white squares > # of black squares)

 

Who said you aren't allowed to put domino stones on top of each other? :mrgreen:

[The Runar]

 

 

 

Everything equals 34 when added up.

 

 

 

Are you sure? ;)

 

 

 

The solution would be:

 

 

 

[hide=]16 | 2 | 3 | 13

 

5 | 11 | 10 | 8

 

9 | 7 | 6 | 12

 

4 | 14 | 15 | 1[/hide]

[A_Mace]

This reminds me of Zeno's paradox of Achilles and the turtle.

 

 

 

They hold a running contest.

 

If the turtle is 10 times as slow as Achilles.

 

And he gets a 100m lead of Achilles.

 

 

 

If Achilles reaches the spot where the turtle started after 10 seconds.

 

In that time the turtle has run 10m.

 

So after 1 second, Achilles has passed those 10 m as well. But in that time the turtle has again travelled 1m.

 

So when Achilles ran that metre, the turtle ran 10 cm.

 

And if Achilles ran that 10 cm, the turtle would have done another...

 

And it goes on like this.

 

 

 

So Achilles will never overtake the turtle.

 

Is this right?

 

 

 

I'll post the answer later.