Chris and Lucy entered a building looking for Manuel. In a room they found a note and a lighted candle. Chris looked at the note and read it aloud:

“Hi! It’s 2:30, and I’m leaving to run some errands. I’ll be back in a couple of hours. BTW, the electricity is out, so I lit a candle for you. — Manuel.”

Then Lucy said, “I know how we can find out how long it’s been since he left! Look, the candle has been burning since he lit it and has a significant amount of wax that’s melted and dripped down. If we figure out what the rate is which the wax is melting and measure the amount of wax that has thus far dripped, we can work backwards to find out how long it has been since he left.”

Chris said, “Why waste your time? The note says he left at 2:30.” Lucy said, “Don’t believe everything you read.” Chris replied, “Look, I’ve known Manuel for a long time, and this is his handwriting. Don’t be ridiculous.”

Lucy replied, “Ah yes, but what does he mean by ‘2:30”? A note like that is subject to interpretation. Suppose he was talking about another time zone or something.” And so a short philosophical argument ensued about the note. However, Lucy prevailed and insisted on performing the measurement and calculations.

A few minutes later, Lucy announced: “Well, I’ve got bad news for us. Based on the amount of wax that has melted and the rate at which the wax is melting, I can confidently tell you that it has been at least one whole day since this guy left. He was probably talking about 2:30 yesterday. And since he said that he’d be back ‘in a couple of hours’, we can assume that something happened to him and he’s not coming back at all. So much for your ‘note’.”

Just then, Manuel walked in. Lucy said, “Are you this guy ‘Manuel”? What took you so long?” Manuel replied, “What are you talking about? I left you guys a note saying I’d be back in a couple of hours. It hasn’t even been that long.” Lucy said, “Never mind the note. I measured the amount of wax that has dripped off your candle, and the rate which the wax was melting. I know you’ve been gone since yesterday.”

Manuel replied, “First of all, that candle isn’t burning anywhere near as brightly as when I first lit it. Second of all, I didn’t light a new candle, but a used one. And thirdly, I used another candle to light this candle and in the process the wax from that candle spilled all over this one.”

Lucy said, “So you set up that candle to deceive us, to make it look like you left the room over a day ago, when in fact it’s been less than a couple of hours.” Manuel replied, “Look, I left you a note telling you when I left. I never intended for you to conduct some silly experiment measuring wax dripping off of a candle to figure out when I left. I put the candle there so you guys would have some light.”

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