During a month with 30 days, a cricket team plays at least one game a day, but no more than 45 games. There must be a period of some number of consecutive days during which the team must play exactly ______ number of games.(a) 17(b) 46(c) 124(d) 24I had been asked this question in examination.I'm obligated to ask this question of Counting topic in portion Counting of Discrete Mathematics

During a month with 30 days, a cricket team plays at least one game a

1.	During a month with 30 days, a cricket team plays at least one game a day, but no more than 45 games. There must be a period of some number of consecutive days during which the team must play exactly ______ number of games.(a) 17(b) 46(c) 124(d) 24I had been asked this question in examination.I'm obligated to ask this question of Counting topic in portion Counting of Discrete Mathematics
Answer» Correct answer is (d) 24 To elaborate: Let a1 be the number of games played until day 1, and so on, AI be the no games played until i. Consider a sequence like a1,a2,…a30where 1≤ai≤45, ∀ai. Add 14 to each element of the sequence we get a new sequence a1+14, a2+14, … A30+14where, 15 ≤ ai+14 ≤ 59, ∀ai. Now we have two sequences 1. a1, a2, …, a30 and 2. a1+14, a2+14, …, a30+14. having 60 elements in total with each elements taking a value ≤ 59. So according to pigeon hole principle, there must be at LEAST two elements taking the same value ≤59 i.e., ai = aj + 14 for some i and j. THEREFORE, there exists at least a period such as aj to ai, in which 14 matches are played.

Discussion

No Comment Found

Related InterviewSolutions

Determine all possibilities for the solution set of a homogeneous system of 4 equations in 4 unknowns.(a) only one(b) finitely many or zero(c) zero(d) one or infinitely manyThe question was posed to me during an internship interview.My question is from Counting in section Counting of Discrete Mathematics
Determine all possibilities for the solution set of a homogeneous system of 6 equations in 5 unknowns.(a) only one(b) zero(c) one or infinitely many(d) finitely manyThe question was posed to me in an interview for job.This is a very interesting question from Counting in section Counting of Discrete Mathematics
In a get-together party, every person present shakes the hand of every other person. If there were 90 handshakes in all, how many persons were present at the party?(a) 15(b) 14(c) 16(d) 17The question was asked in an online interview.The origin of the question is Counting topic in section Counting of Discrete Mathematics
A group of 20 girls plucked a total of 200 oranges. How many oranges can be plucked one of them?(a) 24(b) 10(c) 32(d) 7I had been asked this question in class test.My question is from Counting topic in portion Counting of Discrete Mathematics
Determine the solution for the recurrence relation an = 6an-1−8an-2 provided initial conditions a0=3 and a1=5.(a) an = 4 * 2^n – 3^n(b) an = 3 * 7^n – 5*3^n(c) an = 5 * 7^n(d) an = 3! * 5^nThis question was addressed to me during an interview for a job.This interesting question is from Advanced Counting Techniques in portion Counting of Discrete Mathematics
Determine the value of a2 for the recurrence relation an = 17an-1 + 30n with a0=3.(a) 4387(b) 5484(c) 238(d) 1437I have been asked this question in an online quiz.I need to ask this question from Advanced Counting Techniques in division Counting of Discrete Mathematics
What is the solution to the recurrence relation an=5an-1+6an-2?(a) 2n^2(b) 6n(c) (3/2)n(d) n!*3The question was posed to me in final exam.This interesting question is from Advanced Counting Techniques in division Counting of Discrete Mathematics
Determine the solution for the recurrence relation bn=8bn-1−12bn-2 with b0=3 and b1=4.(a) 7/2*2^n−1/2*6^n(b) 2/3*7^n-5*4^n(c) 4!*6^n(d) 2/8^nThis question was addressed to me during an internship interview.My question comes from Advanced Counting Techniques in portion Counting of Discrete Mathematics
The solution to the recurrence relation an=an-1+2n, with initial term a0=2 are _________(a) 4n+7(b) 2(1+n)(c) 3n^2(d) 5*(n+1)/2I got this question in a national level competition.My enquiry is from Advanced Counting Techniques in division Counting of Discrete Mathematics
Find the value of a4 for the recurrence relation an=2an-1+3, with a0=6.(a) 320(b) 221(c) 141(d) 65The question was asked in an interview for job.This interesting question is from Advanced Counting Techniques topic in section Counting of Discrete Mathematics

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment