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Pick the Winner Correctly
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 X and Y, X the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul...
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Dart Problem
A circular dart board 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 X in the circle. What is the probability that X is closer to the center of the circle than the periphery?
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5 digit number divisible by 4
How many 5 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are divisible by 4?
GANESH
- Oct 13th, 2011
Divisibility rule of 4 is last two digits are divisible by 4 so in 5 digit no last two digit should always be 12,24,32,44,52; (any one of them may be) so for last two digits 5 ways are possible ; si...
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Planet Corba
On planet Corba, 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 formulad = 4 * √ (t - 8) for t ≥ 8where d represents the diameter in mm and t the number of years since the...
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Equidistant Points
Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, What is the number of points equidistant from all the 3 lines?
ranjansaha79
- Dec 26th, 2010
Ans: 1As it is the incenter of the formed triangle which is equidistant from all the three lines...
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Circular Handshake
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}. Find the size of the smallest set of people such that the rest have shaken hands with at least one person in the set.
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Typist's Speed
After the typist writes 12 letters and addresses 12 envelopes, he inserts 1 letter per envelope randomly into the envelopes. What is the probability that exactly 1 letter is inserted in an improper envelope?
Kriti Nassa
- Jan 7th, 2011
0. as 1 letter cannot be in improper envelope. there has to be more than 1 letter that is in improper envelope
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Points on Plane
Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line; i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). Find the maximum value of n1(P) over all configurations P of 10 points in the plane.
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Sheet of Paper
A sheet of paper has statements numbered from 1 to 35. For all values of n from 1 to 35, statement n says "At most n of the statements on this sheet are false". Which statements are true and which are false?
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Min-Max Game
A and B play the following min-max game. Given the expressionN = 12 + X*(Y - Z)where X, Y and Z are variables representing single digits (0 to 9), "A" would like to maximize N while "B" would like to minimize it. Towards this end, "A" chooses a single digit number and "B" substitutes this for a variable of her choice (X, Y or Z). "A" then chooses the next value and "B", the variable to substitute the...
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1/3 of a Number
1/3 of a number is 3 more than 1/6 of the same number. What is the number?
