Alternating Empties

Six glasses are all in a row in front of you, the first three are full of grape juice and the last three are empty. Moving only one glass, how can you make all six alternate between full and empty?

Pour the contents of the second glass into the fifth glass.

Posted in Brain Teasers

Two More Seconds

Ida puts her coffee into the microwave, as she does every morning, for exactly two minutes. When the microwave goes off, she opens the door, but then closes the door again and sets the microwave for two more seconds. What good would two more seconds be?

To rotate the handle on the mug so she can comfortably remove it.

Posted in Brain Teasers

The Ages of a Prince and Princess

A princess is as old as the prince will be when the princess is twice the age that the prince was when the princess’s age was half the sum of their present ages.

What are their ages?

This one took a while to figure out and there are numerous valid ways of finding the answer.

Here is the solution I came up with

I created the following table from the riddle:

 CurrentFuturePast
Princessx2z(x+y)/2
Princeyxz

I then created three equations, since the difference in their age will always be the same.
d = the difference in ages
x – y = d
2z – x = d
x/2 + y/2 – z = d

I then created a matrix and solved it using row reduction.

xyz
1-10d
-102d
.5.5-1d

It reduced to:

xyz
1004d
0103d
0015d/2

This means that you can pick any difference you want (an even one presumably because you want integer ages).
Princess age: 4d
Prince age: 3d

Ages that work

PrincessPrince
43
86
1612
2418
3224
4030
4836
5642
6448
7254
8060

To see other solutions check out the comments from when I posted this on my blog.

Posted in Brain Teasers

A House With No Doors

I am in a house with no doors. There are people inside but give no reply. Who am I?

A fish. A fish bowl or aquarium is the fish’s house and the people inside are the decorative divers that offer no reply (one might ask how the fish knows, given that they aren’t a talkative bunch themselves).

Posted in Riddles

A Smiling Guard

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, “Why are you smiling?”

How did he know his companion was smiling?

They were facing each other. As to why his companion was smiling, the world may never know.

Posted in Brain Teasers

Penny, Cork and A Bottle

Given a corked bottle with only a penny inside, how can you remove the penny without pulling out the cork, breaking the bottle and leaving the cork intact?

Push the cork into the bottle, then shake the penny out.

Posted in Brain Teasers

Ted and The Vicious Dog

Ted was lost while driving around the country and saw a house. He parked under a nearby tree and started toward the house. As soon as he got out of his car a huge dog lunged at him from the opposite side of the tree. Fortunately the dog was chained and Ted managed to stay out of reach. Finding no one home at the house, Ted returned to his car, but as he approached the dog lunged at him again. The chain was so long the snarling animal could reach both car doors. How did Ted escape the dog and get back into his car?

Ted moved slowly around the tree keeping just out of the dog’s reach. The animal followed, winding its chain around the tree until it was too short to reach Ted’s car

Posted in Brain Teasers

Commonly Forgotten And Sometimes Rotten

I am always with you
But commonly forgotten.
You use me constantly,
And can sometimes be rotten.

What am I?

Air.

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

Break, Light, May

What word can be added before or after these words to make a new word or phrase?

Break, Light, May

Day. Daybreak, daylight, may day.

Posted in Riddles