### Brain Teasers

# Stolen Candy Bar

During lunch at school, a group of five boys from Miss Smith's home room visited a nearby canteen. One of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:

1. Chris: "Neither Austin nor I did it."

2. Kraig: "It was Chris or Mark."

3. Mark: "Both Chris and Kraig are lying."

4. Gavin: "Between Chris and Kraig, one of them is lying and the other is speaking the truth."

5. Austin: "What Gavin said is wrong."

When Miss Smith was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Smith is correct, can you determine who took the candy bar?

1. Chris: "Neither Austin nor I did it."

2. Kraig: "It was Chris or Mark."

3. Mark: "Both Chris and Kraig are lying."

4. Gavin: "Between Chris and Kraig, one of them is lying and the other is speaking the truth."

5. Austin: "What Gavin said is wrong."

When Miss Smith was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Smith is correct, can you determine who took the candy bar?

### Hint

Austin's statement is true.### Answer

Mark took the candy bar.Mark is the pivotal character here, since he is either referring to or being referred to by all of the other characters. Use trial and error to solve this:

Option 1:

Mark: Telling the truth. This means:

Chris: Liar

Kraig: Liar

Gavin: Liar

Austin: Truth.

These are the only possible outcomes if Mark tells the truth. Since the teacher said that there are three truth tellers, this solution doesn't work. Therefore, Mark must be a liar.

Option 2:

If Mark is a liar, then there are three options for Chris and Craig: both are truth tellers, Chris lies and Kraig tells the truth, or Chris tells the truth and Kraig lies. If you set up a chart with these options, you can easily determine if Gavin and Austin are telling the truth, too:

Option:..1...2...3

Mark:....L...L...L

Chris:...T...L...T

Kraig:...T...T...L

Gavin:...L...T...T

Austin:..T...L...L

Read these from top to bottom: For example, option 1 is: If Mark lies and Chris and Kraig tell the truth, then Gavin must lie and Austin must tell the truth. Do the same for the other two columns.

The only option here that satisfies the three truth-teller rule is Option 1. Since Chris and Kraig both tell the truth, the thief must be Mark.

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