In a logic system, four switches (A, B, C, D) are either ON or OFF. You know three rules: 1. If A is ON, then B is OFF. 2. If B is OFF, then C is ON. 3. If C is ON, then D is OFF. If switch D is currently ON, what must be the state of switch A?
OFF
Work backward: D is ON, so C cannot be ON (since C ON would force D OFF), meaning C is OFF. Since C is OFF, B cannot be OFF (since B OFF would force C ON), meaning B is ON. Finally, since B is ON, A cannot be ON (since A ON would force B OFF). Thus, switch A must be OFF.
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.
More logic riddles
A merchant has four weights of 1 lb, 3 lb, 9 lb, and 27 lb. Using a traditional two-pan balance scale, what is the single heaviest whole-pound object she can weigh by placing weights on either one or both sides of the scale?
A vault requires a four-digit numerical code. The first digit is double the last digit. The second digit is three less than the first digit. The third digit is the sum of the first and second digits. If the last digit is 2, what is the code?
Four runners—Sam, Leo, Maya, and Nina—finish a race. Nina finished before Sam. Sam finished before Leo. Maya finished immediately after Leo. What was the exact finishing order from 1st to 4th place?
Four runners (Liam, Noah, Emma, and Olivia) finish a sprint. Liam did not come in first or last. Emma finished ahead of Noah. Olivia finished after Liam, but before Noah. Who won the race?
Two trains start moving toward each other at the exact same time from tracks 200 miles apart. Train A travels at 40 mph, and Train B travels at 60 mph. At the same instant Train A starts, a remarkably fast housefly on Train A's front windshield begins flying toward Train B at 80 mph. When the fly hits Train B's windshield, it instantly turns around and flies back toward Train A at 80 mph, continuing this back-and-forth until the two trains collide. What is the total distance the fly traveled?
In a 5-runner race (A, B, C, D, E), A finished ahead of B, but behind C. D finished ahead of C, but behind E. Who finished third?