Varaint of a 10 digit number

Consider a 10-digit number A written as a_1a_2...a_10. A contains each of the digits from 0 to 9 exactly once. The number a_1 is divisible by one. The number a_1a_2 is divisible by two. The number a_1a_2a_3 is divisible by three, and so on...What is A?

A 10 digit number

Consider a 10-digit number A written as a_0a_1a_2...a_9. Now, suppose a_0 is the number of times the digit '0' appears in A; a_1 is the number of times '1' appears in A, and so on... a_9 is the number of times '9' appears. What is A?

Bulbs & Switches

Suppose you have 'n' lightbulbs and 'n' switches that correspond to each of the lightbulbs. Initially, all the lightbulbs are turned off. After you flip a switch, the corresponding lightbulb turns on. If you flip the same switch again, the lightbulb turns off. Each switch corresponds to only 1 lightbulb and vice versa. After 'k' random switches are flipped, what is the expected number of lightbulbs turned on?

Pieces of a Stone

Consider a stone of 'n' kg. What is the minimum number of pieces should the stone be broken so that you can measure all the weights from 1 to 'n' kg in a weighing balance (taraju)? What should be the weight of the each individual piece?

Height of a room

You need to measure the height of an isolated room. There is a bulb hanging from the roof of the room such that it just touches your head while you are in standing position. You are given a meter scale and an alarm clock.

Fly in the Tea

A person went to a restaurant and ordered a cup of tea. A fly fell off in his tea. He asked the waiter to replace it. After a while, the waiter brought a new cup of tea. What should be the strategy of the person to identify whether he has brought the same tea or not. He can take a sip if he wants.

Four Digit Whole Number

Find a four digit number 'n' such that the last 4 digits of n^2 are same as that of n