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Ambiguous PIN Code (Posted on 2010-11-17) Difficulty: 3 of 5
Susan couldn't quite remember her bank PIN code.

She knew:

  • It had 4 or 5 digits.
  • It used 4 or 5 different digits.
  • The first digit is 4 or 5.
  • The second digit is 4 or 5 and none of the other digits is smaller.
  • The number is 4 or 5 times a prime number.
  • If you reverse the order of the digits, the resulting number has 4 or 5 prime factors, all different.
  • In 4 or 5 of these facts, the "4" is the correct number.

What is Susan's PIN code?

See The Solution Submitted by Charlie    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): A Pin that works | Comment 7 of 8 |
(In reply to re(2): A Pin that works by Charlie)

{4454445, 5444445, 5444554, 5454454, 5454544, 5455444}
These were my 5 cases.
I already used the first to find the PIN 5468

Cases 2 and 3 are actually not possible since the number in each begins with 44 the reversal would have 4 as a factor so the prime factors would not all be different.

Case 4 requires checking the 8 primes from 54467/4 to 54988/4 that end in 7 or 9.  None of them work.

Case 5 requires checking the 7 primes from 54675/5 to 54985/5.  None of them work.

Case 6 requires checking the 1 prime from 55678/4 to 55987/4 that ends in a 7 or 9.  That prime is 13967 and does not work because 13967*4 = 55868 which has only 3 different digits.

So the solution that I found is unique (see my other post for a refutation of brolls solution.)

  Posted by Jer on 2010-11-19 16:22:05

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