At the market you can buy a cow for $10, a pig for $1 and 8 hens for $1. How many animals would you need to buy to get 100 mixed animals for exactly $100?
7 cows, 21 pigs and 72 hens. The trick to this is finding the combination of cows and hens with the same cost and quantity since pigs are already equal. The magic combination is 7 cows and 72 hens, giving you 79 animals that cost $79 ($70 + $9). Then you just add 21 pigs to get to 100 animals.
How many country names can you find in the following statements?
Don’t reach in a crack in the rocks, there might be snakes in there.
While I was on the highway called the Alcan, a daily occurrence was car breakdowns.
The top social class, as defined by many, is the upper-upper.
Two children were playing checkers and each played five games. Both children won the same number of games yet there were no ties. How is this possible?
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 woman shoots her husband, then holds him under water for five minutes. Finally, she hangs him. Five minutes later they enjoy a wonderful dinner together. How can this be?