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