If you look you cannot see me. If you see me you cannot see anything else. I can make anything you want happen, but later everything goes back to normal.
I’m a five letter word. Remove my last two letters and I’m a synonym of drag. My second and third letters form an exclamation and my first and second letters are a homophone with a number. What am I?
Towel. Tow is a synonym of drag, ow is an exclamation when you’re hurt (and far more appropriate in mixed company than the four-letter alternatives) and to is a homophone of two.
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.
This creature, part man and part tree, hates the termite as much as the flea. His tracks do not match, and his limbs may detach, but he’s not a strange creature to see.
What has wings but can not fly. Is enclosed, but can outside also lie. Can open itself up or close itself away. Is the place of kings and queens, And doggerel of every means. What is it upon which I stand, Which can lead us to different lands?
My first is twice in apple but not once in tart. My second is in liver but not in heart. My third is in giant and also in ghost. Whole I’m best, when I am roast. What am I?