• Jan 28th 2010, 04:25 AM
Natasha1
I am stuck with this puzzle

I have forgotten my 4 digit PIN number

However, I can remember the following facts:

the first and last digits add up to 10
the first digit is greater than the last digit
the four digits add up to 16
the difference between the last two is 2

QUESTIONS:

Make a list of the 7 possible numbers which fit the facts above.

What is the probability that the 4 digit number had two digits the same?

What is the probability that it is not the correct PIN Number?
• Jan 28th 2010, 06:26 AM
Soroban

Sorry! Misread the problem.
• Jan 28th 2010, 08:29 AM
Natasha1
It can't be.

6154 or 6244 or 6334 or 6514 or 6604 as the difference between the last two digits needs to be 2
• Jan 28th 2010, 09:23 AM
Dinkydoe
Soroban's final answers are correct, but he misread the question.
He used that the difference between first and last number was 2.
We have:

Spoiler:

9**1
8**2
7**3
6**4

As possible pin-numbers combining (1) and (2)

Combining these with (3), (4): Since the first and last number add up to 10. Because of (3) the second and third number must add up to 6.
If we combine that with (4) we find possible numbers:

9331
8602
8242
7513
7153
6424
6064

Then the probability that 2 digits are the same is: $\frac{4}{7}$

The possibility that it's the incorrect number is: $\frac{6}{7}$

Just like Soroban said.

The last question has ofcourse nothing to do with how the numbers look like:

• Feb 12th 2010, 05:47 AM
FengWei
9331, 8242, 7153, 6064, 8602, 7513, 6424