Security code .....
I bought a new Smart Phone this New Year. In this Smart Phone it has a digits security code number. Without Security Code no one can access this phone. I want to give it a strong security code so that every digit of the code is different (like 0123, 1234, 6789 etc.) But for easily remember this security code its sum of digits must be (like 0125, 1034 etc.) How many choices I have left?
The answer is 48.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
We will first consider the possible sets of digits, not taking into account their order.
If the smallest digit is 1 , then the smallest possible sum is 1 + 2 + 3 + 4 = 1 0 > 8 , and so the smallest digit must be 0 .
If the second smallest digit is 2 , then the smallest possible sum is 0 + 2 + 3 + 4 = 9 > 8 , and so the second smallest digit must be 1 .
Now we must find two distinct digits with a sum of 7 . Neither digit may be 0 or 1 , and so the only possibilities for the final two digits are 2 + 5 = 7 and 3 + 4 = 7 . This means that we have narrowed down the security code to two digit sets. { 0 , 1 , 2 , 5 } , { 0 , 1 , 3 , 4 }
To count the possibilities for each digit set, it is a simple permutation of 4 items. Adding up all of the possible security codes, we get, 4 ! + 4 ! = 4 8