Susan couldn't quite remember her bank PIN code.
She knew:
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It had 4 or 5 digits.
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It used 4 or 5 different digits.
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The first digit is 4 or 5.
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The second digit is 4 or 5 and none of the other digits is smaller.
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The number is 4 or 5 times a prime number.
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If you reverse the order of the digits, the resulting number has 4 or 5 prime factors, all different.
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In 4 or 5 of these facts, the "4" is the correct number.
What is Susan's PIN code?
(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.)
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Posted by Jer
on 2010-11-19 16:22:05 |
re(3): A Pin that works
