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# No. of zeros....

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How many zeros are there between 10,000 and 77,777 when written in base 8? Many thanks.

Jun 28, 2018

#1
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Well, thanks to heureka, we can use his wonderful formula for this instead of actually counting them!!.
[(n - 1) x (b - 1) x (b^n - 1)] / b, where n=number of digits, and b=base used.
[(5 - 1) x (8 - 1) x (8^(5 - 1))] / 8 =
[   4      x      7     x    4,096] / 8   =
114,688 / 8                  =14,336 zeros between 10,000 and 77,777 in base 8.                  [Amazingly beautiful formula !!!. Thanks heureka]

Jun 28, 2018

#1
+2

Well, thanks to heureka, we can use his wonderful formula for this instead of actually counting them!!.
[(n - 1) x (b - 1) x (b^n - 1)] / b, where n=number of digits, and b=base used.
[(5 - 1) x (8 - 1) x (8^(5 - 1))] / 8 =
[   4      x      7     x    4,096] / 8   =
114,688 / 8                  =14,336 zeros between 10,000 and 77,777 in base 8.                  [Amazingly beautiful formula !!!. Thanks heureka]

Guest Jun 28, 2018
#2
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Thank you Guest heureka  Jun 29, 2018