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ALIo

Guest

numbers of sequences we can do !

How many sequences ( x1 , x2 ,x3 , x4 , x5 , x6 ) can we make from { 1 , 2 , 3 , 4 , 5 , 6 } so that :
x1 ≤ x2 ≤ x3 ≤ x4 ≤ x5 ≤ x6

thanks everybody

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: numbers of sequences we can do !

Do you mean to say that 'x' is a constant which is multiplied by the numbers in the sequence?
If so, then inequality holds for all x ≥ 0.

HallsofIvy

Guest

Re: numbers of sequences we can do !

How many sequences ( x1 , x2 ,x3 , x4 , x5 , x6 ) can we make from { 1 , 2 , 3 , 4 , 5 , 6 } so that :
x1 ≤ x2 ≤ x3 ≤ x4 ≤ x5 ≤ x6

thanks everybody

If mean sequences of those six numbers, in increasing order, then the answer is 1: {1, 2, 3, 4, 5, 6} itself!  Any other sequence would change the order so the numbers would not be increasing.  That seems rather obvious.  Perhaps I am misunderstanding.

ALIo

Guest

Re: numbers of sequences we can do !

maybe this was unclear ( x1 , x2 ,x3 , x4 , x5 , x6 )
i meant : ( x , y , z , l , h , m ) like this ...

Zhylliolom

Real Member

Registered: 2005-09-05

Posts: 412

Re: numbers of sequences we can do !

If mean sequences of those six numbers, in increasing order, then the answer is 1: {1, 2, 3, 4, 5, 6} itself!  Any other sequence would change the order so the numbers would not be increasing.  That seems rather obvious.  Perhaps I am misunderstanding.

I would imagine sequences such as (1, 1, 1, 1, 1, 1), (1, 1, 2, 2, 3, 3), etc. would work as well. The requirement is x[sub]1[/sub] ≤ x[sub]2[/sub] ≤ x[sub]3[/sub] ≤ x[sub]4[/sub] ≤ x[sub]5[/sub] ≤ x[sub]6[/sub], not x[sub]1[/sub] < x[sub]2[/sub] < x[sub]3[/sub] < x[sub]4[/sub] < x[sub]5[/sub] < x[sub]6[/sub]. So try looking at it again.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: numbers of sequences we can do !

I couldn't think of an easy way to work out the answer, so I just brute-forced it in Excel.

I get 462 of them.

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Why did the vector cross the road?
It wanted to be normal.