You’ve just purchased a roll of tokens. The roll is eight tokens high and nine tokens long. Can you work out how many times you have to break the roll up so that it is separated into individual tokens?
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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 .
hope this helps. ......
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 .
hope this helps. ......
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