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Alok is attending a workshop "How to do more with less" and today's theme is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as woman kind) had only worked with fewer digits.
The problem posed at the end of the workshop is

1) How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4?
Can you help Alok find the answer?

2) Alice and Bob play the following coins-on-a-stack game. 20 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns.

A turn consists of moving the coin on the top to a position i below the top coin (0 ≤ i ≤ 20).
We will call this an i-move (thus a 0-move implies doing nothing).

The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on ubsequent turns neither player can make a 2-move. If the gold coin happens to be on top when it's a player's turn then the player wins the game. Initially, the gold coinis the third coin from the top. Then Alice has no winning strategy.

In order to win, Alice's first move should be a 0-move.
In order to win, Alice's first move should be a 1-move.

3) A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle.

What is the probability that Q is closer to the center of the circle than the periphery?

4) 36 people {a1, a2, ..., a36}meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}.  Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

5) The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India.  At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate.

Suppose 12 such programmers take 12 minutes to write 12 lines of code in total.
How long will it take 72 programmers to write 72 lines of code in total?

6) After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

7) A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, statement n says: 'Exactly and of the statements on this sheet are false.' Which statements are true and which are false?

The 39th statement is true and the rest are false. All the statements are false.
The odd numbered statements are true and the even numbered statements are false.
The even numbered statements are true and the odd numbered statements are false

8) A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement and says "At least n of the statements on this sheet are true." Which statements are true and which are false?

The odd numbered statements are true and the even numbered are false.
The first 26 statements are false and the rest are true.
The even numbered statements are true and the odd numbered are false.
The first 13 statements are true and the rest are false.

9) 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty.
The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The right most person is not questioned. Which of the following possibilities are true?

A. All suspects are lying or the leftmost suspect is innocent.
B. All suspects are lying and the leftmost suspect is innocent .
Neither A nor B
Both A and B
B only
A only

10) Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is

11) The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?


12) 10 people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ......, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ......, {ak-1, ak}, {ak, a1}shake hands).

13) For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning.

Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?

14) On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids called echina start growing on the rocks. echina grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula
d = 4 * √ (t - 8) for t ≥ 8

Where the represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. How many years back did the solar blast occur?

15) Alok and Bhanu play the following min-max game. Given the expression

N = 9 + X + Y - Z

Where X, Y and Z are variables representing single digits (0 to 9),Alok would like to maximize N while Bhanu would like to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable.

Assuming both play to their optimal strategies, the value of N at the end of the game would be

16) Lion and tiger are there. Lion lies on Monday, Tues, Wends and Tiger lies on Thurs, Frid, Sat. Lion said that today is one of those days when I lies. Tiger said that today is one of those days when I lie too. Then find today?
1/3 rd of a number is more 3 than the 1/6th of a number then find the number?

Learn the conpects of the questins these questions are repeating by changing the values.