A four-character passcode is made by choosing each character from the digits 1 to 6, repeats being allowed. How many such passcodes use at least one digit more than once?

Count everything, then take away the well-behaved case. All passcodes: each of the 4 places has 6 choices, so $6^4=1296$. Passcodes with every digit different: $6\times 5\times 4\times 3=360$. Hence at least one repeat = 1296 − 360 = 936. Trap 360 reports the complement instead of the answer — the classic 'forgot to subtract from the total' slip. Trap 1296 ignores the condition. Trap $720=6\times C(4,2)\times 5\times 4$ counts only the tidiest kind of repeat, one digit used exactly twice with two further distinct digits filling the other places, and so misses codes such as 3335 and 2255.