Question

You just bought a big bar of chocolate! The bar is eight pieces high and nine pieces long. Can you work out how many times you have to break the bar so that it is separated into individual squares?

Answer 1

The following is a problem of permutation and combination

Now,

To find the number of ways, the basic idea is to seprate the rectangle into smaller squares and then apply the formula for number of squares

= n(n+1)(2n+1)/6

(Sigma of n²)

Now,

Since the values are quite big 8 and 9

We will use the direct formula for calculating the number of squares

=m(m+1)(2m+1)/6 + (n-m)(m)(m+1)/2

=(8×9×17)/6 + (1×8×9)/2

=204+36240

So, the job can be done in 240 ways

Hope this helps !!!!!!!!!!