A man is found dead at the end of an alley. A detective who enters the scene sees the letter X and immediately knows who killed the man and why. What did the detective conclude?
The alley is a bowling alley. The man who was killed was a pin spotter (an old profession where they would reset the pins by hand). The X was the marking on the score sheet for a strike. The detective saw the letter X and knew that the person bowled last, got a strike, and was due to bowl again. But they bowled before the pin spotter could get out of the way.
Four. If the apples are A, B, and C, it’s possible that you could take out one A, one B and one C with three apples, but the fourth apple must be one of the three kinds.
A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He comes to a river and needs to cross it, he finds a small boat that can carry only him and one animal, how does he get himself, the fox and two chickens across the river safely?
Take the fox over, return with nothing. Go over with one chicken, return with the fox. Go over with the second chicken, return with nothing. Finally, take the fox over.
A pearl. They’re found underwater. Removing the head (p) leaves Earl, a guy who could be at your door. Removing the tail (l) leaves pear, a fruit and if you cut both off you’re left with ear, which is with you because it’s attached to your head.
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.