Question

A deck of 1000 cards is numbered with whole numbers from 1 to 1000, with each card having just one
number. How many of these cards do not have a zero in their number? (please be detailed)

Answer 1

Total number of cards in the deck is 1000.

Now out of 1-100 numbered cards, 10,20,30,40,50,60,70,80,90,100 numbered cards are the only 10 cards which have zero(es) in their number.

Out of 101-200 numbered cards, there are 19 cards with 0 in their numbers( that are 101,102,...,109,110,120,...,190,200).

Similarly out of 201-300, there are 19 cards with 0 in their numbers ( that are 201,...209,210,220,...290,300).

Similarly 19 cards with 0 are between 301-400,401-500,501-600,...,901-1000.

So in total, number of cards with zero in their numbers is 10+19*9 = 181.

So number of cards with no zero in their numbers is 1000-181 = 819.

Hence answer is 819.

Hope the solution helps. Thank you.

(Please comment if further help is needed)