Number Probability

Tsrnc2

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Feb 14, 2019
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My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?
 

Subhotosh Khan

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Jun 18, 2007
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My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?
How many 4-digit numbers are there with all four numbers same (e.g. 1111 or 7777, etc.)?

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pka

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Jan 29, 2005
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My bank has a policy of disallowing certain pin numbers. Pins are the standard 4 digits. Pins that have all the same digit (1111), a sequence of digits forward or reverse (1234, 4321), as well as pins that start with 19 or 20 (1999) are disallowed. A 4 digit pin has 10,000 possible pins minus those disallowed. My questions is how many allowed pin possibilities exist?
We cannot have \(\displaystyle (XXXX)\) where \(\displaystyle X\) is digit. So how many are there?

Let's see, we cannot have \(\displaystyle (19XY)\) where \(\displaystyle X~\&~Y\) are digits. So how many are there?
Now we need to double that number. Why is that?

How many increasing strings of four are there? Did you include \(\displaystyle \large\bf 0123~?\)
Now we need to double that number. Why is that?

Please post your answers so they can be checked.​
 
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