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?
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?
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.
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:
Current
Future
Past
Princess
x
2z
(x+y)/2
Prince
y
x
z
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.
x
y
z
1
-1
0
d
-1
0
2
d
.5
.5
-1
d
It reduced to:
x
y
z
1
0
0
4d
0
1
0
3d
0
0
1
5d/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
Princess
Prince
4
3
8
6
16
12
24
18
32
24
40
30
48
36
56
42
64
48
72
54
80
60
To see other solutions check out the comments from when I posted this on my blog.
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).
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?”
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?
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