I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

What occurs twice in a week, once in a year but never in a day?

I shave every day, but my beard stays the same. What am I?

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

The dirtier I get, the whiter I look. Who am I?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

Suppose you are sitting in an interview and the interviewee asks you an aptitude question.

You have three buckets with a capacity of 4 litres, 8 litres and 10 litres and you have a large tank of water. Now you have to measure 3 litres of water precisely using those buckets. How will you do it?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

The LCD device should be able to tell the right time in the format HH:MM: SS in a 12-hour format. You can refer to the picture to get an idea. The device is a simple "level indicator" which has to be converted into a watch. How will you program it to work?