malungkids great at maths
Just now
Aanan is breaking a chocolate bar into smal
pieces. At every step, he breaks a piece eith
horizontally or vertically:
Eventually, only 1 x 1 chocolate pieces are left.
If the size of the original bar was 10 x 5, ho
many steps (breaks) did this take Aanan?
cth
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Answers
Given:
Aanan is breaking a chocolate bar into small pieces. At every step, he breaks a piece eith horizontally or vertically: Eventually, only 1 x 1 chocolate pieces are left.
To find:
If the size of the original bar was 10 x 5, how many steps (breaks) did this take Aanan?
Solution:
For a chocolate of size m × n, we need mn - 1 steps.
By breaking an existing piece horizontally or vertically, we merely increase the total number of pieces by one.
Starting from 1 piece, we need mn - 1 steps to get to mn pieces.
Therefore, for given, we have,
10 × 5 is the original size of the chocolate bar.
The number of steps Aanan take to reduce the number of chocolate piece to 1 × 1 is,
= mn - 1
= 10 × 5 - 1
= 50 - 1
= 49
Therefore, a total of 49 steps are required.