Five Points, Ten Distances

Five points, A, B, C, D, and E, lie on a line. The distances between them in ascending order are: 2, 5, 6, 8, 9, X, 15, 17, 20, and 22. What is X?

We assume that the points are ordered A to E from left to right. We have AE = 22 and either AD = 20, BE = 17, or AD = 17, BE = 20. Without loss of generality AD = 20, BE = 17, and therefore AB = 5, BD = 15, DE = 2. The distance of 6 is associated with either BC or CD, and therefore the points are arranged in one of these two ways:

  1. AB = 5, BC = 6, CD = 9, DE = 2
  2. AB = 5, BC = 9, CD = 6, DE = 2

If it is the latter, we get the sequence of distances: 2, 5, 6, 9, 11, 14, 15, 17, 20, 22, which does not fit the provided sequence.

If it is the former, we get the sequence of distances: 2, 5, 6, 8, 9, 14, 15, 17, 20, 22, and therefore X = 14.

Wacky Wordies 2

Can you figure out what phrases and sayings are represented in the Wacky Wordies below?

The answers are:

  1. Leave no stone unturned
  2. Foot in the door
  3. Go on a double-date
  4. Green with envy
  5. Look square in the eye
  6. Broken promise
  7. Pull up alongside the curb
  8. Excuse me
  9. High-grade performance
  10. Take on a big job
  11. Split the difference
  12. He came out of nowhere
  13. Wait on hand and foot
  14. Suit to a T
  15. Know it forward and back
  16. A period in history
  17. Crooked lawyer
  18. Get up on the wrong side of bed
  19. Sign on the dotted line
  20. Disorderly conduct

The Gun and the Recording

One day, the police finds a dead man inside a hut, with a bullet in his head. In his left hand, the man is holding a gun. In his right hand, he has a recording. When the recording is played, the police hears the man talking about how horrible his life has been and how he wanted it to end. The recording ends with a gunshot. The police are about to call it a suicide until a detective points out an important clue. What is it?

If the person shot himself and died, he wouldn’t have been able to stop the device from recording further.

Rewarded and Fired

A very rich man has many servants in his mansion. One day as he is about to travel, his night watchman warns him not to board his flight. “I had a dream last night that the plane crashed,” the watchman tells him. The rich man is annoyed at first, but since he is also superstitious himself, he decides not to take the flight.

Later that day as he is watching the news, he sees that his plane did, in fact, crash. He goes over to thank and reward his servant, and then fires him. Why?

The watchman has been sleeping at work instead of guarding the mansion, so that’s the reason he gets fired.

Barbenheimer Tickets

Barbara and Oprah went to a theater where two movies were being shown: “The Barbie Movie” and “Oppenheimer”. The ticket price for the former was $15 and the ticket price for the latter was $20. When Barbara handed $20 to the cashier, she was asked which movie she wanted to watch, to which she replied, “The Barbie Movie”. However, when Oprah handed $20 to the cashier, she was automatically given a ticket for “Oppenheimer”. How come?

Barbara handed two $10 bills, so the cashier wasn’t sure which movie she wanted to watch. However, Oprah handed four $5 bills, so it was clear she wanted to watch “Oppenheimer” (otherwise she would have handed just three $5 bills).