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Problem re: bases and powers

I was having a read through the Siklos problems in core mathematics booklet and I struggle with this problem's solution.

"A postman delivers to in a street of houses numbered from 1 to 1000, given that he refuses to deliver to houses with the digit 9 in the number, how many houses does he deliver to?"

Solution spoiler tagged for anybody who wants to answer.

Spoiler


I don't understand what the significance of the power is, and why it relates to the number of digits and gives a correct solution. Can somebody please explain?
Original post by Asurat
I don't understand what the significance of the power is, and why it relates to the number of digits and gives a correct solution. Can somebody please explain?

Hi Asurat

If 9 is not included, you have the digits 0,1,2,3,4,5,6,7,8; 9 digits in total.

For a two digit number, you then have 9 x 9 possible arrangements.

For a three digit number, you have 9 x 9 x 9 possible arrangements.
000, 001, 002, 003, 004, 005, 006, 007, 008
010, 011, 012, 013, 014, 015, 016, 017, 018,
...
880, 881, 882, 883, 884, 885, 886, 887, 888
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Asurat
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Original post by M.C. Math
Hi Asurat

If 9 is not included, you have the digits 0,1,2,3,4,5,6,7,8; 9 digits in total.

For a two digit number, you then have 9 x 9 possible arrangements.

For a three digit number, you have 9 x 9 x 9 possible arrangements.
000, 001, 002, 003, 004, 005, 006, 007, 008
010, 011, 012, 013, 014, 015, 016, 017, 018,
...
880, 881, 882, 883, 884, 885, 886, 887, 888

That makes sense, thank you!

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