My instructor is a sadist

[Phrophetsam]

Bored from answering the problem set, Jenny suddenly writes the natural numbers from 1 to
1001 in a row.

(a) Can the signs "+" and "-" be placed between the numbers in such a way that the value
of the resulting expression is 100? If yes, show an example. If not, show the reason why.

(b) How about -499? If yes, show an example. If not, show the reason why.

Is he expecting me to be able to write down every number from 1-1001 and then do this by trial and error. there has to be a better way to do it right?

 

[Dr.Peterson]

The better way is to think! (That's what math is all about: finding easier ways to do things by thinking first.)

Can you find the sum of all 1001 numbers (using a formula you may know)?

Now think about what happens to the sum if you change any one + to -.

 

[Steven G]

No, your instructor I am sure prefers that you do not write down all the numbers from 1-1001. S/he want you to be clever about how you figure it out.
Even in the end you do not have to write all numbers between between 1 and 1001
For example: Your answer might look like (1-2+3-4+....+99) + (100 + 1001 +....+ 230) - (231+232) + (233-234+235-236+....+1001) and I did not write down all the numbers.

An instructor that makes you think is NOT a sadist!