Question

You'hv just purchased a bar of tokens for the gaming machine. the bar is eight tokens high and nine tokens long. Can u work out how many times you have available to break the bar up so that it is separated into individual bars?

Answer 1

Final Answer : 71

Given : A 8 x 9 matrix like bar .

Asked : No. of times we have to break(along the line of square) line the bar of 8 x 9 matrix to convert it into 1 x 1 small matrix (token) .

Solution:
1) If there is only one square token of 1 x 1 matrix , then we don't need any breaks.

2) If there is one 1 x 9 bar, then clearly we need to break it 8 times to bring 1 x 1 small token.
This is also equal to :
No. of small squares - 1 = (9* 1-1) = 8

2) If there is one 2 x 9 bar, then first we need to break it into two 1 x 9 bar,then these two bars into small 1 x 1 tokens.
Hence, we need to break it into : 1 + 8 +8 = 17 times.
This is also equal to
= > No. of small squares ( 1 x 1) - 1 = 2 *9 -1 = 17

3) Hence, by INDUCTION HYPOTHESIS,
To break 8 x 9 bar into small 1 x 1 small squares, we need to break it into :
=>No. of small squares - 1
=> (8* 9 -1)
=> 72-1 = 71 .

Hence, we need to break it 71 times.