Lying On Certain Days of the Week

Angel lies on Mondays, Tuesdays and Wednesdays but tells the truth the rest of the week.

Brenda lies on Thursdays, Fridays and Saturdays, but tells the truth every other day.

Angel says, “Yesterday I was lying.”

Brenda replies, “So was I.”

What day was it?

Thursday.

Putting the information in a table makes it easier to solve. We’ll use A for Angie, B for Brenda, T for truth and F (false) for lying.

 SMTWThFS
ATFFFTTT
BTTTTFFF

To begin with, there aren’t any days where both of them told the truth and lied the day before, so we know one of them must be lying.

So we have two options, either Angel is lying or Brenda is.

Option 1. Angel is lying.

In order for this to be the case, she needs to be lying today and telling the truth yesterday, so we need two days in a row with T F. And if Brenda is telling the truth, she would need two days with F T. That means we’re looking for two days that have

Angie:  T F
Brenda: F T

Option 2. Brenda is lying.

This is just the reverse of the above, so we need to find:

Angie:  F T
Brenda: T F

The only day that matches either of the two options is Thursday, and it’s option 2. Brenda is the liar.

Posted in Brain Teasers

What Digit Does Each Letter Represent?

This is what you know:

1. Each letter represents a different digit from 1 to 9
2. The total of each row is 17.
3. (B × B) + B + F = A
4. C × F = EF (a 2-digit number, not their product)

A B C
D E F

What digit does each letter represent?

A = 7
B = 1
C = 9

D = 8
E = 4
F = 5

A + B + C = 17
D + E + F = 17
B2 + B + F = A
C × F = EF

To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.

2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.

C × F = EF
9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.

Posted in Brain Teasers

When Set Loose I Fly Away

When set loose
I fly away,
Never so cursed
As when I go astray.

A fart.

Posted in Riddles

What Gets Wetter As It Dries?

What gets wetter as it dries?

A towel.

Posted in Riddles

Longest AIOTS word

What is the longest word you can find using only the letters AIOTS (each letter can be used any number of times)?

Tattooists, which has 10 letters.

Posted in Brain Teasers

The Empty Pocket

How can your pants pocket be empty but still have something in it?

It has a hole. The hole is the thing (although it could be argued a pocket has air, darkness or dust and so on).

Posted in Brain Teasers

Special Two Letter Combinations

What do these three letter combinations have in common?

DE
HI
MN

Hint: These combinations don’t have it in common.

AK
IN
WY

They are the only three US state abbreviations whose two letters are next to each other in the alphabet.

DE – Delaware
HI – Hawaii
MN – Minnesota

Posted in Brain Teasers

Three Items for $100

Bill buys three items at the store for exactly $100. The second item costs half as much as the first item, and the third item is half as much as the second.

How much did each one cost?

First: $57.14
Second: $28.57
Third: $14.29

Posted in Brain Teasers

Don’t Get a Goat

On a game show there are three closed doors – one hides a car and the other two conceal a goat. The contestant selects a door, which remains closed, and the host, knowing where the car is hidden, reveals a goat behind one of the remaining two doors. The contestant is then given the option to switch doors or stay with the one they originally selected. What should the contestant do to have the best chance of winning the car?

The contestant should switch doors, which doubles the chance of winning the car. Initially there is a 2/3 chance of picking a goat, but once the other goat is revealed, switching to remaining door gives the contestant a better chance of winning the car. This is known as the Monty Hall Problem and can be very unintuitive.

Posted in Brain Teasers

Kevin’s School Supplies

Kevin brings his school supplies to the counter. The cashier rings up his purchase for a total of $1.70. Kevin is puzzled, and says, “I bought 2 pencils at 2 cents each, 5 pencils at 4 cents each and 8 notebooks and 12 sheets of colored paper. I don’t remember the prices of the latter two, but the total can’t be $1.70.”

How did Kevin know?

Because 4 cents, 20 cents, 8 notebooks and 12 sheets of colored paper are all divisible by 4, but 170 cents isn’t.

Posted in Brain Teasers