One letter can be used to replace the first letter of each word pair below to create two new English words. The new letters can then be combined to spell a word. What is that word?
MAIL ____ PINK
CART ____ SAID
GRID ____ RIMLESS
LINK ____ BOUND
ROWED ____ RIPPLE
A boat has a ladder that has six rungs. Each rung is one foot apart. The bottom rung is one foot from the water. The tide rises at 12 inches every 15 minutes. High tide peaks in one hour.
When the tide is at its highest, how many rungs are under water?
I am here, I am there
I am burned into the mind of none
I walk on fire and live on ice
My words are meaningless for I talk not
I hate everyone yet fear no one
I have lived for centuries
Yet I have never existed
What am I?
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.
In addition to the two hands on the end of their arms, they also have three hands of cards. Another alternative could be handwriting, of which most people have one, but that could be added into the mix.