Solution:

Brian is the one who speaks truth.

Adam is lying about Brian. Also Cody Is lying since Brian does not lie. Thus Brian is the one speaking truth. Any other combination will fail to come out true.

Solution:

7 Races.

Solution:

Align the toothpicks to form TEN. Use one toothpick for each of the lines.

Solution:

Either your read from start or from ends, it will be same

Solution:

16

Explanation:
9 [1x1] squares
5 [2x2] squares
1 [4x4] square
1 [4x4] square

9 + 5 + 1 + 1 = 16 squares.

Solution:

16-days

In 15-days, he will climb 15-inch and when he climbs 5 inch more, he will be out of the well :-)

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

'five'

Its the count of alphabet

Solution:

The three errors are as follows:
a) fynd is spelled wrong. The correct spelling is 'find'.
b) that is not appropriate to use here. It should be 'this'.
c) There are only two errors in the question and that is the third error because the questions asks us to find three.

Solution:

1 2 3 4 5 6 and 7 8 6

Since summation of numbers 1-9(1 2 3 4 5 6 7 8 9) is 45 , so its impossible to divide into two equal parts.
Since we cant flip over 6 to make it 9 but we can flip 9 to make it 6 and hence the solution

Solution:

A cigar stuck in the wall