Postman quick question

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Apostman 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?

My working: From 0-100 he doesn't deliver to 10 houses, from 100-200 he doesn't deliver to 19 houses, 200-300 he doesnt deliver to 19 houses, 300-400 he doesnt deliver to 19 houses, from 400-500 he doesnt deliver to 19 house, from 500-600 he doesnt deliver to 19 houses, from 600-700 he doesnt deliver to 19 houses, from 700-800 he doesnt deliver to 19 houses, from 800-899 he doesnt deliver to 19 houses, from 900-100 he doesnt deliver to 99 houses.

adding them up you get 261 so 1000 - 261 you get 739. Is this correct? My friend told me it is 9^3 i.e 729, but i have no idea how he done that, could anyone explain?
 

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  • #2
SammyS
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Apostman 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?

My working: From 0-100 he doesn't deliver to 10 houses, from 100-200 he doesn't deliver to 19 houses, 200-300 he doesnt deliver to 19 houses, 300-400 he doesnt deliver to 19 houses, from 400-500 he doesnt deliver to 19 house, from 500-600 he doesnt deliver to 19 houses, from 600-700 he doesnt deliver to 19 houses, from 700-800 he doesnt deliver to 19 houses, from 800-899 he doesnt deliver to 19 houses, from 900-100 he doesnt deliver to 99 houses.

adding them up you get 261 so 1000 - 261 you get 739. Is this correct? My friend told me it is 9^3 i.e 729, but i have no idea how he done that, could anyone explain?
Why 729?

How many three digit numbers are there using only the nine digits, 0 through 8 ?
 
  • #3
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My working: From 0-100 he doesn't deliver to 10 houses,
Are you sure?
from 100-200 he doesn't deliver to 19 houses, 200-300 he doesnt deliver to 19 houses, 300-400 he doesnt deliver to 19 houses, from 400-500 he doesnt deliver to 19 house, from 500-600 he doesnt deliver to 19 houses, from 600-700 he doesnt deliver to 19 houses, from 700-800 he doesnt deliver to 19 houses, from 800-899 he doesnt deliver to 19 houses,
Correct. :smile:
from 900-100 he doesnt deliver to 99 houses.
Are you sure? (Even allowing for the fact that you made a typo with writing "900-100" instead of "900-1000".)
 

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