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.
54325. Rather than being a mathematical solution, the answer is derived by prepending (putting in front of) the value on the left side of the equation with the previous answer. So for 3 you take 25, the previous answer, and put 3 in front, giving you 325. Then you put 4 in front to get 4325 and lastly, put 5 in front to get 54325.
The tree is in the middle of the road as measured by length, not in the middle of it by width. In other words, the tree is growing on the side of the road, but it is equidistant from either end of the road, and therefore in the middle.
This makes it quite easy to pass the tree as you just drive on the road, unless you’re texting and you run into said tree. If this is the case, stop texting.
Everyone has it. Those who have it least don’t know that they have it. Those who have it most wish they had less of it, but not too little or none at all.
Age. Young children don’t even know their age and extremely old folks wish they could turn back the hands of time, but not so much that they’re too young or they no longer have an age at all.
An electric train is traveling on a 2000-mile journey from Chicago, IL to Los Angeles, CA. It has 16 cars with a total of 320 passengers. The weather is cloudy and cool, with a warm front approaching from the south. Which direction will the steam blow?
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 beggar’s brother went out to sea and drowned. But the drowned man had no brother. What was the relationship between the man who drowned and the beggar?