You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

What number should come in place of the question mark below?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

As you can see that fifteen matches have been used to form an arrangement. What you have to do is remove any six of them to make them ten.

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?