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

Guest 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

#1**+2 **

Best Answer

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