Answer to Question #104672 in Math for andrea

Question

in the olden days, type was set by hand using lead pieces. the type had to be carefully put together. the printer wants to print a list of whole numbers from 1 to 1,000 in order to find the primes under 1,000. if he had 100 of each of the digits from 0 to 9 , how many numbers could he set before he ran out of some digits?

Answer 1

As we know that , prime number is the number which can be divide by 1 and itself .

So as per the question requirement we have to find the number of prime number which printer can print between 1 and 1000

so we will use the given below algorithm for this and it has also given one condition that from digit 0 to 9 there are 100 of number are coming

so as between 0 to 9 there are total 10 digit and we are getting as 100

so , for 10 digits we are getting 100 digit

here total number of terms can be 100 and common dfference to form a series will be 10 a= 100

use the concept, Sn= $\frac{n}{2}(2a+(n-1)d)$

so total terms will be

Sn= 50(200+990)

Sn= 59500

so total number may be of 59500 before run out digit