Gary: red cap, left in a station wagon, bought a lamp
Linda: red cap, left in a station wagon, bought paperbacks
Frank: straw hat, left in a pickup, bought a lamp
Donna: no hat, left in a station wagon, bought paperbacks
Ray: red cap, left on a bicycle, bought paperbacks
Beth: straw hat, left in a pickup, bought paperbacks
Exactly one of the six bought the console. Three witnesses each describe a different detail of the buyer:
Mrs. Pruitt, next door: “The buyer wore a red cap.”
Mr. Lowell, across the street: “The buyer drove away in a station wagon.”
Tommy Kessler, age 12: “The buyer also bought a lamp from me.”
The patrolman is sure of one thing: exactly one of the three witnesses is lying, and the other two are telling the truth. Who bought the stolen console?
💡 Hint
Score each shopper by how many of the three statements would be true if that shopper were the buyer. The count must match exactly two true and one false.
Reveal answer
Linda bought the console. Mrs. Pruitt and Mr. Lowell told the truth, and Tommy Kessler was the one who was mistaken or lying.
Step-by-step solution
- If a shopper were the buyer, every statement matching that shopper would be true. Exactly two statements are true, so the buyer must match exactly two of the three statements: red cap, station wagon, bought a lamp.
- Score each shopper. Gary: red cap, wagon and lamp, so all three are true. Linda: red cap and wagon true, lamp false, so two. Frank: only the lamp is true, so one. Donna: only the wagon is true, so one. Ray: only the red cap is true, so one. Beth: nothing is true, so zero.
- Gary matches everything, which would mean nobody is lying. That conflicts with the patrolman’s fact, so Gary cannot be the buyer, however neatly he fits.
- Frank, Donna and Ray would each require two witnesses to be lying, and Beth would require all three. That also conflicts with the fact that exactly one lies.
- Only Linda leaves exactly one false statement. She wore a red cap and left in a wagon, but she bought paperbacks, not a lamp. So Tommy’s statement is the false one. Checking all six shoppers against all three statements shows Linda is the only possible buyer.
Why it fools people
The perfect match is a gift to the lazy mind: it fits everything we were told, so we stop. The detail that spoils it is the rule that someone is lying. A witness statement set with a known liar must contain a contradiction, and a suspect who creates no contradiction is the wrong person. The lesson carries over to real reasoning: when a rule says the evidence is imperfect, an answer that fits perfectly should make you suspicious, not satisfied.
Did you get it?
About This Puzzle
On a bright Saturday in the summer of 1985, the families of a quiet cul-de-sac in suburban Ohio held their yearly yard sale. Folding tables, lawn chairs and handwritten price tags lined every driveway. The Kessler family sold a video game console to someone in the crowd, and only later learned that it had been reported stolen from a house on the next street. Their twelve-year-old son had worked the table, and the neighbors had noticed the shoppers. A patrolman now wants the buyer, and he has three witnesses and one problem: one of them is not telling the truth.
How to Think About It
Don’t ask which witness seems the most believable. Instead, turn each shopper into a score. For every person, count how many of the three statements would be true if that person were the buyer. Then apply the one fact you are certain of: exactly two statements are true and one is false. Only a shopper whose score matches that pattern can be the buyer. Make a small table with the three statements across the top and the six names down the side, and mark each cell true or false. The right row will stand out.
Common Traps
The strongest trap is the shopper who matches all three descriptions. It feels like a perfect fit, and the instinct says that is your buyer. But the patrolman has told you one witness is lying, so a perfect match is actually impossible. Another trap is picking whichever witness seems nervous or whichever statement sounds most casual. Several shoppers can contradict one statement; the question is which contradicts exactly one.
Where This Puzzle Comes From
Puzzles with several witnesses and a fixed number of liars are a standard form of logic puzzle. They appear in knights-and-knaves style problems and in many mystery collections, where the solver tests each possible culprit against the statements. This one is an original construction, set in the era of cul-de-sacs and folding tables.
Try This Variation
Suppose the neighbors correct their notes: Gary actually bought paperbacks, not a lamp. Everything else, including the three statements and the rule that exactly one witness lies, stays the same. Can you still name the buyer?
Show the answer to the variation
No. Now Gary has a red cap and a station wagon but no lamp, which makes him match exactly two statements, just as Linda does. Both fit, and in both worlds it is Tommy who is wrong. With the notes corrected, the case needs one more clue to separate Gary from Linda.