Finding the Smallest Natural Number in a Series of Calculations

[sutupidmath]

let * be either + or - ( you can use both of them)

then let 1*2*3*4*.....*2004*2005*2006

The question is this, what would be the smallest natural number that you would get, after you do the necessary calculations?

i got the answer 1.
here is what i did:

(2006-2005)-(2004-2003)-...-(4-3)+(2-1)=1

so can anyone please comment on my approach?

thnx

 

[matt grime]

Such as what? 1 is the smallest natural number for most people (for some it is 0). Though I don't think you have the minus signs quite right. What you've written appears to go, after simplifying brackets

1-1-...-1+1, which is really about -998. But you have a good idea.

 

[sutupidmath]

what if i go like this then:
(2006-2005)-(2004-2003)+(2002-2001)-(2000-1999)+...+(6-5)-(4-3)+(2-1)=1

But how would know whether 1 or zero or any other result is the right answer

1-1+1-1+1-1+1-1+...+1-1+1=1

 

[matt grime]

You're asked to find the smallest natural number. Since you can find 1, and that is commonly taken to be the smallest natural number, then what is it you want to ask?

 

[sutupidmath]

i want to know that, how can i be sure that my way of solving the problem is correct, and ishould not approach the problem differently instead?
thnx

 

[matt grime]

But you've found, by a perfectly valid method, that you can get 1, and since 1 is (for the purposes of this question) the smallest natural number, we are done. There really isn't anything to worry about. There is no such thing as *the* way to solve a question that you must use (unless instructed to do so explicitly in the question e.g. "prove by induction that..."). But there are no constraints here.

 

[sutupidmath]

thank you indeed