Math Is Fun Forum

Welcome!

Darn, he's RIGHT!

OK, try this:

In the library there is an "encyclopedia of worms". It is three volumes long, each volume has exactly 1000 pages and they are placed neatly on the shelf side-by-side. It takes the worm one hour to chew through 100 pages and it takes half an hour to chew through a cover.

If the worm starts at Page One of the First Volume and chews through to Page 1000 of the Last Volume, how long does it take?

Warning: I don't know the answer, but I know that there are possible wrong assumptions.

Thats great!

Thanks, Milos ...

TEAMWORK !

Cool ... I will leave it for someone else then ...

Good luck.

For simplicity, let's call sqrt(x+1) "A" and sqrt(x-1) "B"

You have: (A+B)/(A-B) = (4x-1)/2

Multiply both sides by (A+B)*(A-B):    (A+B)*(A-B) * (A+B)/(A-B) = (A+B)*(A-B) *  (4x-1)/2

Cancel: (A+B)^2 = (A+B)*(A-B) *  (4x-1)/2

Expand: A^2 + 2AB + B^2 = (A^2 - B^2) * (4x-1)/2

Substitute A^2 = (x+1) and B^2 = (x-1): (x+1) + 2AB + (x-1) = ((x+1) - (x-1)) * (4x-1)/2

Simplify: 2x + 2AB = 2 * (4x-1)/2

More: 2x + 2AB = 4x - 1

More: 2AB = 2x - 1

Good ON you !

Easy puzzles?

You are either too smart, or I need to make up some harder puzzles ! 

Off the top of my head, you can do it with one multiplication. Middle-Value times N.

If N=5 then SUM = 1+2+3+4+5 = 15, using my idea the middle is 3, and 3 x 5 = 15
If N=6 then SUM = 1+2+3+4+5+6 = 21, using my idea the middle is 3.5 (half-way between 3 and 4) , and 3.5 x 6 = 21

This could be generalized as (Stt+End)/2 * (End-Stt+1)
where Stt=1 and End=N for your needs.

Let us try this one:

3+4+5+6=18
Using (Stt+End)/2 * (End-Stt+1): (3+6)/2 * (6-3+1) = 4.5 * 4 = 18

For your N=1000 case we would have (1+1000)/2 * (1000-1+1) = 500.5 * 1000 = 500,500

TADA !

Moby > Eminem

(Holy Cow)

Did you just do your KS3 Sats, Rora?