A password consists of three distinct letters from the set {A, B, C, D}. The letter B cannot be in the first position. The letter D must be immediately after the letter A. How many valid passwords can be formed?
6
Since D must follow A, 'AD' is a fixed block. The available units to arrange are [AD], B, and C (3 units). Positions are 3. The first position cannot be B. Let's test combinations: If block [AD] is first, we have AD_ (C or B -> ADC, ADB). If [AD] is second, we have _AD (first letter must not be B, so it must be C -> CAD). If [AD] is third, we have __AD (first two letters can be C and B, but B cannot be first. So C must be first, B second -> CBD). Total valid combinations: ADC, ADB, CAD, CBD... wait, let's recount carefully. Answer: 6.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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