A clock loses exactly 2 minutes every single hour. Exactly at midnight, it is set to the correct time. What will be the true, correct time when this clock next shows midnight?
1:00 AM the following day
The clock loses 2 minutes per hour, so it loses 48 minutes every 24 hours. To make up a full 12-hour (720-minute) cycle to look like midnight again, it needs to lose 720 minutes. 720 / 48 = 15 days. After 15 days, the clock will read midnight, but it will have fallen 15 hours behind. Midnight + 15 hours = 3:00 PM? Wait. Let's recalculate carefully: The clock loses 2 minutes every hour. In 24 hours, it loses 48 minutes. It needs to lose 720 minutes (12 hours) to show the same hands again. 720 / 48 = 15 days. Wait, if it loses 2 minutes an hour, when it reads 12:00, how much real time has passed? Real time elapsed = X. Clock time = X - (2/60)*X = (58/60)X. We want Clock time to be 12 hours behind real time? No, to show midnight again, it must have lost 12 hours relative to a normal clock, or 24 hours? A standard 12-hour clock face shows midnight twice a day. Let's look at relative drift. After 30 days, it has lost 30 * 48 = 1440 minutes = 24 hours. After 30 days, it is exactly 24 hours behind, meaning it matches the correct time again. Wait, if it's 24 hours behind, it shows midnight at the exact same moment a real clock shows midnight. Let's check the wording: 'What will be the true, correct time when this clock next shows midnight?' After 30 days, the real clock reads midnight, and the slow clock also reads midnight. So the true time is midnight 30 days later. Let's use a simpler one or check if 30 days is correct. Yes, 30 days * 48 min = 1440 min = 24 hours.
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
In a hallway, 100 closed lockers numbered 1 to 100 undergo 100 passes. On pass 1, every locker is toggled (opened). On pass 2, every 2nd locker is toggled. On pass 3, every 3rd locker is toggled, continuing this pattern until pass 100 where only locker 100 is toggled. After all passes, which lockers remain open?
Four players—W, X, Y, and Z—participated in a chess tournament where each played every other player once. There were no ties. W beat X, Y, and Z. X beat Y and Z. Y beat Z. How many matches did X win?
A courier must deliver four distinct parcels (A, B, C, and D) across a grid, but strict routing protocols apply. Parcel A must be delivered before B. Parcel C cannot be delivered until D has reached its destination. If B is delivered before C, what is the absolute last parcel that can possibly be delivered?
I am a bridge with neither piers nor cables, built by nature's quiet hands. I span across the winter fields, yet melt away when day expands. What am I?
Three friends—Leo, Maya, and Sam—each wear a shirt of a different color: red, blue, or green. Maya is not wearing red. Leo is wearing the color that is alphabetically first among the three available colors. What color shirt is Sam wearing?
Three boxes are labeled 'Apples', 'Oranges', and 'Mixed'. You know that EVERY box is incorrectly labeled. You pick one fruit from the box labeled 'Mixed' without looking inside, and it is an Apple. What are the correct contents of all three boxes?