# Guessing a three digit pin code from an 8 key keypad

• MHB
• jridgeman99
In summary, the conversation discusses a problem involving a thief trying to guess a three digit PIN code from an 8 key keypad. It is unclear if it is a permutation or combination problem and the question is posed about the probability of guessing correctly on the first try. The conversation also mentions the fundamental counting principle and the importance of considering the order of the digits in the PIN code.
jridgeman99
Hello, the problem is as follows. I'm not sure if it is a permutation or combination problem. It says if a thief steals and ATM card and must randomly guess the correct three digit pin code from an 8 key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

jridgeman99 said:
Hello, the problem is as follows. I'm not sure if it is a permutation or combination problem. It says if a thief steals and ATM card and must randomly guess the correct three digit pin code from an 8 key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

How many PIN codes are possible...can you apply the fundamental counting principle to answer this question?

I'll just add on to Mark's comment that PINs are order-sensitive. 123 is not the same as 321.

## 1. How many possible combinations are there for a three digit pin code on an 8 key keypad?

There are 512 possible combinations for a three digit pin code on an 8 key keypad. This is because there are 8 options for the first digit, 8 options for the second digit, and 8 options for the third digit, resulting in 8x8x8=512 possible combinations.

## 2. What is the probability of guessing a correct three digit pin code on the first try?

The probability of guessing a correct three digit pin code on the first try is 1/512, or approximately 0.2%. This is because there is only one correct combination out of 512 possible combinations.

## 3. How many attempts would it take on average to guess a correct three digit pin code on an 8 key keypad?

On average, it would take 256 attempts to guess a correct three digit pin code on an 8 key keypad. This is because the probability of guessing correctly on any given attempt is 1/512, so it would take approximately 256 attempts to reach a 50% chance of guessing correctly.

## 4. Is there a way to increase the chances of guessing a correct three digit pin code on an 8 key keypad?

Yes, there are a few ways to increase the chances of guessing a correct three digit pin code on an 8 key keypad. One way is to use a pattern or sequence that is commonly used for pin codes, such as birthdays or repeating numbers. Another way is to try variations of commonly used pin codes, such as adding or subtracting 1 from each digit.

## 5. How does the number of keys on the keypad affect the difficulty of guessing a three digit pin code?

The more keys on the keypad, the more difficult it is to guess a three digit pin code. This is because the number of possible combinations increases exponentially with each additional key. For example, a 10 key keypad would have 1,000 possible combinations for a three digit pin code, while a 12 key keypad would have 1,728 possible combinations.

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