21,086 views

Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either $635$ or $674,$ the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?

1. $1000$
2. $2430$
3. $3402$
4. $3006$

635_ _ _ _

OR

674_ _ _ _

 First 3 digit 4th digit 5th digit 6th digit 7th digit No. of trial & error 635 1 way (can place only no. 9) 9 ways (can place 0 to 8 no.s) 9 ways (can place 0 to 8 no.s) 4 ways (can place 1/3/5/7) 1*9*9*4 = 324 635 9 ways (can place 0 to 8 no.s) 1 way (can place only no. 9) 9 ways (can place 0 to 8 no.s) 4 ways (can place 1/3/5/7) 9*1*9*4 = 324 635 9 ways (can place 0 to 8 no.s) 9 ways (can place 0 to 8 no.s) 1 way (can place only no. 9) 4 ways (can place 1/3/5/7) 9*9*1*4 = 324 635 9 ways (can place 0 to 8 no.s) 9 ways (can place 0 to 8 no.s) 9 ways (can place 0 to 8 no.s) 1 way (can place only no. 9) 9*9*9*1 = 729

The total no. of Trial and Error process with 635 as prefix is (324 + 324 + 324 + 729) = 1701.

This 1701 combinations will repeat with 674 as prefix also.

Minimum no. of trials = 1701 + 1701

= 3402 (option 3)

5.4k points

1 vote
1
1,265 views
2
3
383 views
4
208 views