A spy encounters a keypad that requires a 4 digit PIN. He uses a fine dust to find which keys are used in the combination. He does not know the sequence of keys, nor which ones repeat if any. Obviously if only 3 keys are required one of them is repeated. If 2 keys are required then either 2 keys are repeated twice, or 1 key repeated three times.
The puzzle is for me to design a pin which makes the spies job as hard as possible. Are 4 unique keys the safest, or is have one or more repeating keys better?
- One digit used = 1 combination
- Two digits used = 14 combinations = 2^4-2
- Three digits used = ? combinations
- Four digits used = ? combinations
Can someone do the math and come up with the possible combinations that use exactly 3 and 4 keys, no more or less. My intuition is that the repeating keys will increase the number of combinations more than used all 4 keys for the pin.
PS. For the two digits (if they are
Y) then the combinations are:
XXXY, XXYX, XXYY, XYXX, XYXY, XYYX, XYYY, YXXX, YXXY, YXYX, YXYY, YYXX, YYXY, YYYX