Logic Puzzles

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A man buys a rope from a woman for $3.00 and hands the woman a $10 bill. The woman goes into the grocery store next door to get change. She returns and gives the man $7.00. After the man leaves, the clerk from the store comes and says, “Hey, that was a counterfeit bill you gave me.” The woman gives the clerk a good bill. How much has the woman lost?
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Two hours ago it was as long after one o’clock in the afternoon as it was before one o’clock in the morning. What time is it now?
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If place 1 cake of soap on a pan of a scale and 3/4 cake of soap and a 3/4-pound weight on the other, the pans balance. How much does a cake of soap weigh?
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You and your friend are trapped in a space prison on an alien planet. The alien warden decides to give you and your friend a chance at freedom. He states that your friend shall be allowed to temporarily leave your cell and try to escape through an electric gate guarded by a 3-number passcode. If your friend answers incorrectly or says anything but the final answer, your friend will be thrown back in the prison. A computer will then tell your friend 4 clues if requested. If this passcode is properly answered, you and your friend shall be freed. You are then blindfolded and your friend leaves. You hear your friend walk down one of the numbered hallways to the gate. Your friend asks for the first clue. A voice answers, “The numbers are in ascending order so that the number is greater than or equal to the number before it.” Your friend asks for the second clue. The voice says, “The product of the 3 numbers is 36.” Your friend asks for the third clue. The voice says, “The sum of the numbers is the number of the hallway you entered.” Your friend pauses for a moment and thinks. Your friend then asks for the fourth and final clue. The voice says, “The largest number only appears once in the code.” You hear a beep. You hear your cell door swing open. You are free! What was the code?
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I have three envelopes, into one of them I put a $20 note. I lay the envelopes out on a table in front of me and allow you to pick one envelope. You hold but do not open this envelope. I then take one of the envelopes from the table, demonstrate to you that it was empty, screw it up and throw it away. The question is would you rather stick with the envelope you have selected or exchange it for the one on the table. Why? What would be the expected value to you of the exchange?
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Morgan was making apricot jam. She put all the apricots in the pot and stirred them up. Then she remembered she had to add 1 ounce of lemon juice for every two apricots! How did she figure out how much lemon juice to put?
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