Melody

I like 17 too cause it is one third of 51

Thank you Alan,

I shall think on this :)

(x+6)(x+8)

=x(x+8)        +6(x+8)

=x*x+x*8     +6*x+6*8

= x^2+8x      +6x+48

= x^2+14x+48

-9 x (-8)=+72

I am thinking of a positive number, less than 500, that is divisible by every number from 1 to 10 (inclusive), with one exception. What number am I thinking of? Prove that the answer is unique.

Mmm

well if it is divisable by 10 then it is divisable by 2 and 5 as well      10,2,5

If it is divisavle by 9 then it is divisable by 3                                     9,3

If it is divisable by 8 then it is divisable by 4 and 2 as well                8,4,2

If it is divisable by 6 then it is divisable by 3 and 2 as well

All numbers are diviable by 1

So I am probably looking for a number that is not divisable by 7 but is divisable by all the others

Lets see

10*9*8*6=4320     Mmm     that is a bit bigger than 500    

The lowest common multiple of 6 and 9 is 18

The lowest common multiple of 8 and 10 is 40

18*40=720      Still too big

18=2*3*3       and 40 = 2*2*2*5

So the lowest common multiple of 18 and 40 is  2*2*2*5*3*3 = 360

So I do believe that the number you seek is 360.

Now 360 is the smallest common multiple of 1,234,5,6,8,9 and 10  

But it is not divisable by 7.

I am convinced that this is the only number that meets all these criteria but I don't know how to set out a proof 

Hi Mellie

It is good to see you again :))

factor(10!-1)

$${factor}{\left({\mathtt{10}}{!}{\mathtt{\,-\,}}{\mathtt{1}}\right)} = {\mathtt{29}}{\mathtt{\,\times\,}}{\mathtt{125\,131}}$$

$${factor}{\left({\mathtt{11}}{!}\right)} = {{\mathtt{2}}}^{{\mathtt{8}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{11}}$$

These two numbers are realtively prime, the only factor that they have in common is 1

I do not understand what you are trying to show with this graph Radix   

I have added this inot this probability/counting thread.

Yes well Nauseated, I do not know which moderator you would  be referring too.

I think you took a wrong turn and stumbled into the wrong forum :/