My New Taxi Cab Number.
I got a new mobile number which is of the form
######1729
. If you want to contact me by randomly inserting the missing digits, then what is the maximum no. of wrong attempts that you may face while trying to contact me.
Details And Assumptions :
Total no. of digits in my mobile number is 10.
Provided that the number you will try inserting (######) is divisible by .
The mobile no. does not start with Zero (0).
No other conditions applied.
The answer is 520.
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1 solution
First, let us check the number of multiples of 1729 which are less than 999999
1 7 2 9 9 9 9 9 9 9 = 5 7 8 . 3 6 8 . . .
This means that there are 578 multiples of 1729 less than 999999.
But, as the number is of 10 digits, we have to exclude all multiples less than 100000
1 7 2 9 1 0 0 0 0 0 = 5 7 . 8 3 6 . . .
There are 57 multiples of 1792 which are less than 100000.
So, there should be a total of 578 – 57 = 521 possible numbers.
Out of these, as there must be a correct number, the maximum number of wrong attempts is 520.